stoppableforce mentioned some of the changes. I'd like to go into more detail and analysis.

General

• Re-balanced XP. The amount of XP to gain levels has been re-adjusted to better mesh with the character wealth by level charts (e.g. Starting gold vs 13.33 encounters of thr appropriate CR's worth of treasure). This means that after 5th level, it requires more than 1000 * level to get the next level. There are also fast and slow XP charts now (x2/3 and x4/3 required/level).
• Combat Maneuvers. Trip, sunder, etc. have been re-balanced into combat maneuvers that utilize a Combat Maneuver base (usually the same a BAB). When trying to trip a person, you make a Combat Maneuver Attack vs that persons Combat Maneuver Defense. This works like attack vs AC. It's a much improved system and the Advanced Player's Guide [APG] adds some additional maneuvers. So far the combat maneuvers are: trip, sunder, grapple, bull rush, disarm, overrun, drag (pulls a creature), reposition (relocates a creature within your reach), dirty trick (applies short-term conditions), steal (snatches objects from the target).
• Favored Class. No XP penalty for multiclassing, but a level in your favored class is worth 1 hp or 1 skill point. The APG has additional options based on class and race. E.g.: an half-orc sorcerer may choose to get +1/2 point of damage to fire spells (rounded down). That is, if he chooses this options for two levels, he gets a net +1 damage with fire damage spells.
• XP Cost. Item creation feats and spells no longer have XP costs; it's all gold now.
• Encounter Level. Better rules for determining CR. Each monster is worth a fixed XP amount to be divided evenly among players. Allows for fine tuning of encounters.

Feats

• Are granted at every odd level.
• Feats like Power Attack are now less flexible but simpler and with better value. Deadly Aim has been introduced to provide the same Power Attack feature with ranged weapons.
• Cleave is far less circumstantial and became a separate exploit.
• There are no/fewer dead feats. Toughness gives +1 hp per level (and the first 3 hps are granted upfront at 1st level) so it's useful. Dodge is a plain +1 dodge AC versus all opponents. Skill augmenting feats (like Alertness or Animal Affinity) give +2 to a couple of skills but improve to a +4 if you have 10 ranks in that skill.

Skill System

• Some skills have been aggregated. Relevant examples are Perception and Stealth.
• There is no 1st-level x4-kicker: if you are a Rogue you get (8 + Int modifier) skill points per level. So a 1st level, non-human Rogue with Int 10 has exactly 8 skill points (or 9 if Rogue is her favorite class and she chooses to invest there). This is balanced by the fact that if you have at least one rank in a class skill you get a +3 bonus in that skill.
• There are no 1/2 ranks. Spending a skill point in cross-class skills gives you a full rank (but you don't get the +3 bonus).
• Permanent modification to your Intelligence score may cause you to lose or gain skill points.
• Maximum ranks are equal to your hit dice.

Races

• Dwarf. +2 Con, +2 Wis, -2 Cha.
• Elf. +2 Dex, +2 Int, -2 Con. +2 to caster level checks to overcome spell resistance, +2 to Spellcraft checks to identify properties of magic items.
• Gnome. +2 Con, +2 Cha, -2 Str. Gnome magic tricks based on Charisma. +2 to Perception, +2 to a Craft or Profession skill.
• Half-Elf. +2 one ability score. Bonus Skill Focus feat. +2 to Perception. Immune to sleep and +2 to saves versus enchantment effects. 2 favored classes instead of 1.
• Halfling. +2 Dex, +2 Cha, -2 Str.
• Half-Orc. +2 one ability score. +2 to Intimidate. One last round as disabled when brought below 0 hit points.
• Human. +2 one ability score. +1 Feat at level 1. +1 skill point per level.

Classes

• More Options. Most classes have a list of specific class features from which you can cherry-pick from (like the 3.5e's Rogue talent, but much more varied and awarded starting at much lower levels). Expect more diverse characters.
• Class Features. All class features' save DCs goes up with level (10 + 1/2 class level + ability mod.). Monster's saves are not generally sky-high, so the features have a chance to connect.
• Very Few Dead Levels. Most empty lines in the class tables have been filled up with something. Some full casters (Clerics, Sorcerers and Wizards) still have levels where the only new feature is a new spell slot.
• Caster Level. All caster classes have caster level equal to their level.
• Cantrips and Orisons. 0-level spells now are more like at-will abilities. Wizards/Clerics/Druids memorize them as normal, but casting them doesn't make the caster forget the spell. Sorcerers have infinite 0th level slots but limited known.
• Hit Dice. Some classes have been promoted (bolded, below)
  • d12: Barbarian
  • d10: Fighter, Paladin, Ranger
  • d8: Bard, Cleric, Druid, Monk, Rogue
  • d6: Sorcerer, Wizard
• One Level Dipping Multi-classing in a class for only a single level is, in most classes, less useful than it used to be. Many of the features have been spread across multiple levels or are based on class levels.
• 20th Level Capstone. A class specific, powerful ability is only available at 20th level. Since PF does not have epic-rules yet (not that these are hard to import), single-classing is sexier than before.
• No Multiclass Penalty. Paladin and Monk restrictions are a thing of the past. XP penalties are gone too.

Barbarian

• Rage. More flexible: counted in rounds per day, rather than times per day.
• Rage Powers. Their ability list encompasses powers (a bit more powerful than feats) usable only during rage.
• Damage Reduction. Is awarded earlier and goes up better.

Bard

• HD: d8.
• Bardic Knowledge. Simply adds 1/2 level to Knowledge skills and lets a Bard perform Knowledge checks even if untrained.
• Bardic Performance. Better/more clear rules on types of performances that count for bardic performance. Expanded list of performances; some of them escalate with level. Deadly performance as 20th level capstone. The Perform skill ranks requirement has been dropped.
• Versatile Performance. For a Bard, each Perform skill can act as a double for two other skills (e.g.: Perform (Act) can be used in place of a Bluff or Disguise check, Perform (Percussion) in place of a Handle Animal or Intimidate check). This does not mean he has to actually play an instrument, but simply that he can use the skill bonus of another skill.
• A Knack with Skills. Bards have diverse new features that interact with skills. From being able to ignore the trained requisite, gaining all skills as class skills, and taking 10 even when not allowed, up to taking 20 on Knowledge checks up to 3 times per day.
• Good Feat Support. Arcane Strike and other feats allow a Bard to become much more effective in armed combat. So you're not dead weight or a fifth wheel.

Cleric

• Proficiency. They are no longer proficient with heavy armor.
• Domain Powers. Increased in power and have level-dependent effects (usually a second ability that kicks in at 6-8th). The most frequent powers granted at 1st level are touch or range attacks that deal about 1d6 + 1/2 cleric level. The benefit of +1 to caster level on related spells is no longer a given.
• Channel Energy. The old turn/rebuke became a 30 ft. burst of positive or negative energy that heals or inflicts 1d6/odd level damage to nearby creatures. Feats allow you to selectively exclude targets. Channel feats as normal (but the list of feats is pretty different). Turn and rebuke are not a default for Clerics; they have to acquire the relevant feat.

Druid

• Wild Shape. Awarded earlier and its usages per day go up more frequently. At 20th level Druids can wild shape at will. All shapechange spells are more precise in what abilities you gain. Physical stats of the wild shape comes as a bonus to character's ones: not as a replacement. This goes along with a complete overhaul of the form-shifting spells.
• Animal Companion. Can be substituted for access to a Cleric domain (and domain spells) chosen among Air, Animal, Earth, Fire, Plant, Water, and Weather. The animal companion option, however, is pretty good.

Fighter

• Retraining. At 4th and every other 4th level thereafter, a fighter can trade out a bonus feat he has for a new one as long that old feat isn't being used as a prerequisite.
• Bravery. A bonus to Will saves vs fear that goes up with level.
• Weapon Training. Bonuses on weapon groups (a +1 to attack and damage that goes up to +4 at 17th level). Additional weapon group training is awarded later with decreasing bonuses (like the Ranger's favored enemy). At 20th chooses a weapon and gain +1 to critical multiplier, automatic threat confirmation and immunity to disarm with that weapon.
• Armor Training. Reduces armor check penalty and increases maximum Dexterity bonus (both advantages go up with level up to +4). No speed reduction in medium armor; and later, none in heavy armor either. At 19th damage reduction 5/- when armored or wielding a shield.

Monk

• Flurry of Blows. Treated as two weapon fighting with no off hand and BAB equal to Monk level instead of 3/4 level. At 20th his flurry breakdown is +18/+18/+13/+13/+8/+8/+3. Can use combat maneuvers instead of attacks with a CMA equal to the above BAB.
• Maneuvers. After 3rd level, uses Monk level instead of BAB for combat maneuvers.
• Bonus Feats. Awarded at 1st, 2nd, 6th, 10th, 14th, and 18th from a custom list (narrower than the Fighter's one).
• Ki Pool. Is a set of ki points that increase with level. Ki points could be expended for additional attacks or temporary bonus to AC, and later to fuel supernatural abilities such as incredible jumps, self-healing, dimension door or etherealness.

Paladin

• Channel Energy. As a good Cleric, but relies on Lay on Hands uses instead.
• Smite Evil. Lasts the entire fight, provides a bonus to AC too, and hurts evil dragons and evil outsiders more. Up to 7 times per day at 19th.
• Divine Bond. Either a special mount or a holy spirit that inhabit and buffs the Paladin's weapon.
• Lay on Hands. Numbered uses per day that increase with level. Each use cures 1d6/odd level. Standard action on others, free action on self.
• Mercies. Additional rider effects on Lay on Hands that removes fell conditions (cure disease, remove curse, remove blindness/deafness, etc.).
• Aura. Additional auras (of Justice, of Resolve, etc.) automatically granted at certain level. They grant additional bonuses and options to self and allies within 10 ft.
• Spells. Now are Charisma-based; Wisdom is no longer a favorite ability for Paladins.
• Holy Champion. At 20th level Paladin heals maximum amount of damage (60) with Lay on Hands or Channel Energy, and Smite Evil banishes the target if it is an evil outsider.

Ranger

• HD: d10.
• Favored Enemy. The granted bonus to damage is not precision-based (it is meaningful against creatures immune to critical hits and at any range).
• Combat Style. At 2nd, 6th, 10th, 14th and 18th picks a bonus feat from a list that is tied to the chosen style. Styles are two-weapon combat or archery; APG adds crossbow, mounted combat, natural weapon, two-handed weapon, and weapon and shield.
• Hunter's Bond. Either an animal companion (which is no longer a worse version of the Druid's) or the ability to grant allies half the Ranger's damage and to hit bonus vs favored enemies.
• Quarry. Select a designated foe. Can track at full speed and gets extra combat bonus against.
• Favored Terrain. Can select favored terrains (such as forest, cold, urban, underground, etc.) that grant bonuses on initiative and some skills. Up to 4 terrain types at 18th level.
• Master Hunter. 20th level capstone feature grants a possible death attack once per day against each favored enemy type (doesn't matter if the target is quarry or not).

Rogue

• HD: d8.
• Rogue Talent. Every even level they can cherry pick a rogue-specific trick. Talents are divided in normal (2nd to 8th) and advanced (10th to 20th). Many of these talents kick in when applying sneak attack damage.
• Trapfinding. A plain +1/2 level to Perception and Disable Device skill checks relating to traps. They also can disable magic traps.
• Trap Sense. An increasing dodge bonus (up to +6) to AC and Reflex against trap attacks.
• Master Strike. 20th level capstone is a death, paralysis or sleep effect delivered through every sneak attack.

Sorcerer

• HD: d6.
• Bloodline. Sorcerers select a bloodline at 1st level (like arcane, draconic, fey, etc.). Each bloodline provides 5 powers (including the 20th level capstone), a list of spells that are automatically added to the Sorcerer's repertoire, and a knack with certain kind of spells.
• No Familiar. Except for the arcane bloodline.

Wizard

• HD: d6.
• Arcane Bond. Either a familiar or a bonded object (ring, wand, staff, etc.). The object allows casting of a spell in spellbook 1/day even if you haven't memorized it.
• Arcane School. A specialist Wizard must use two slots to memorize a spell from an opposed school (select two). Each specialization brings two additional abilities at 1st level, plus another that kicks in at 6th or 8th. Universalist Wizards also gain one ability at 1st level (a minor telekinesis) and the ability to apply a metamagic feat on a spell on the fly at 8th.

Advanced Player's Guide

Provides a lot of additional options.

6 More Core Classes

• Alchemist. Bombs, potions, and mutagens ("Dr. Jekyll and Mr. Hyde" abilities).
• Cavalier. A mounted knight, similar to Paladin in devotion to a concept, but tied to a chivalrous order instead of a religious one. Gains and provides teamwork skills.
• Inquisitor. A different take on a holy fighter than Paladin. An Inquisitor enters sacred stances called Judgments that boost combat skills. A scourge to heretics.
• Oracle. A different take on divine caster. Has dramatically different domain-like abilities (called mysteries). Comes with a curse that wrecks their body or spirit but provides crescent abilities.
• Summoner. An arcane caster with special abilities tied to the summoning aspect. Also, a point buy summoned/spiritual companion that is the main focus of the class.
• Witch. An arcane caster getting power through a familiar. Drastically different spell list than wizard (cure spells). Has hexes (one of which acts like true resurrection).

And also:

• Additional Favored Class Options. Depending upon your race and class; expand your options when taking a level in your favored class (beyond the core +1 hp or +1 skill point).
• Alternate Race Traits. Trade off base racial traits with new ones (of the same race). Examples: dwarven Hatred trait (bonuses against orcs and goblinoids) can be traded for the Ancient Enemy trait (bonuses against drow), halfling Keen Senses can be traded for Low Blow (+1 on critical confirmation rolls against target larger than themselves), human bonus skill points can be traded for Heart of the Streets (+1 to Reflex and AC when adjacent to at least 2 allies, and crowds are not difficult terrain for them).
• Alternate Kits. Trade off a set of base class features with a set of new ones (of the same class). Examples: archer fighter, cloistered cleric, scout rogue, scroll scholar wizard, hospitaler paladin, arcane duelist bard.
• Traits. Mini-feats (e.g.: +1 to hit when in surprise round) that are more often story hooks than abilities (in general 2 at first level).
• Hero Points. Rare points that allow for astonishing effects (stave off a spell for 1 round, perform an additional action, reroll a crucial die, etc.). Collected at level up and as additional rewards from the GM.
• Teamwork Feats. Great bonuses that only apply if your friends also have them.

What this Means

• More power. Characters' power level has been tuned up. In particular, they seems to be more resilient.
• Item creation changes. Expect your players to actually use these feats now. You wizard will craft wands, etc. and will make items for 1/2 price. Be prepared to deal with it.
• Combat Maneuvers. Expect people, Monks especially, to opt for tripping/grappling etc. since it's worth it now and is much easier to calculate.
• Sorcerer, Monk, Fighter fixes. People may stick with these classes since they don't suck anymore.
• No multiclass penalties. Expect more multiclass characters. Perhaps even triple/quadruple classes?
• Capstone abilities. Alternatively, no multclassing since 20th level ability is so nice for each class.
• Animal Sidekick alternative. No more useless mount/animal companion if you run primarily dungeon crawls.
• Shape change. GM's life is easier. Harder to dump physical stats. No more CoDZilla.
• Channel Energy. This will come into play a lot more. Clerics can heal a large number of people using this ability. So can Paladins. They can also burn a large number of zombies. Plan accordingly.

Paizo has managed to take virtually every aspect of 3.0/3.5 and tweak/rewrite it to work faster and be more balanced. They managed to bring choice and variation of abilities to every single class (some more than others, still). With the Advanced Player's Guide they introduce 6 classes that are all balanced and playable with the 11 core classes, giving 17 core classes.

Long time player of ArM5 here, with my recollections:

3rd edition to 4th

The largest differences are those not listed on page 262 of ArM4 Core. The publisher changed from White wolf to Atlas and therefore the fundamental assumptions behind the game changed.

Mechanical

The largest change, in my opinion is that ArM4 has "spell boosting" where you can burn vis for an extremely non-trivial range, duration, or target increase. This changes the balance of power of magi in mythic europe.

Setting

In ArM3, due to a desire to be [somewhat compatible][1] with other white wolf products, there's True Reason as an Aura and virtue that's pretty silly. Basically it's taking enlightenment concepts and trying to push them back in time. House Guernicus is known as Quaesator, due to their most common role. Virtues and flaws have a different balance. There's a link between Tremere in ArM and Tremere in WoD. Confidence operates as reroll instead of bonus.

I'm sure there are other, subtle, differences, but the largest are in the feel of the setting. The difference in publishers makes a significant change to the tone of the game.

4th to 5th

The differences from 4th to 5th are, as the core book says on 223, "Nothing has changed ... Everything has changed" And it's completely correct. The setting changes from 3rd to 4th are mostly gone, though with a few humorous notes: "The Tremere had a problem with vampires. They fixed it. It's not interesting now." Which is riffing on the white wolf stuff.

Setting

Functionally speaking, there are no setting changes that I can tell, and I'm quite familiar with 4th and 5th. While it's possible to use setting books from any edition due to the... rough familiarity of editions, setting books from 3rd and below require "interpretation" that books and adventures from 4th don't. Adventures from 4th are almost wholly compatible, due to the whole "monsters have built-in powers" things. When adapting adventures, power down the opposition, but they can be run from the books as-is.

The largest change in setting comes from the supplements (Art and Academe is a must buy for anyone interested in that time period. City and Guild is a horrible supplement.) There is a much lower focus on "magic" in the world and more focus on the world qua itself. This complements the absence of vis-boosting which means magi cannot trivially take out mundane armies, especially with Realms of Power: The Divine in play. The world as presented is open to significant amounts of interpretation, just like in earlier editions, which suggests the ability to dial for whatever game you want to play. (My current game is mostly focused on resource management and survival in a hostile political atmosphere, and I'm happy to share how I figured out highly-granular accounting schemes for the covenant in a different post if poeple are interested.)

Mechanics

One of the more striking "everything changed" aspects is in virtues. The point system (thankfully) was abolished and virtues consolidated into major and minor. With the exception of Beserk (minor virtue, should be major flaw in how it works out in game play) there are no "trapped" virtues or flaws like previous editions sported. Spell Guidelines have been rationalized and consolidated very well, tough the ranges, durations, and targets have changed slightly (for the better.) There are fewer ones, but spells are roughly at the same power level. Vis is far far less useful in spellcasting and rituals generate long-term fatigue, so they are profoundly not spammable. The changes guide is an excellent reference due to the lack of setting changes.

One of the larger mechanical changes that will impact how players think about the game is confidence. In 4th ed, if you had enough confidence, you could spend it all on every roll and, barring a botch, always succeed and get it back. In 5th, confidence is split into Confidence Score and confidence points (and roughly each realm has an [Hierarchy (Infernal),True Faith(Divine),Fable(Faerie)) score to reflect increasing affiliation with that realm. The magic realm doesn't have a unique one, which reflects the centrality of the core book. Players earn confidence points by role playing and can spend them (as the rules are written) on any stress die roll that happens for a specific event. I run with the house rule that confidence can be spent on anything, which significantly ramps up the rate of power increase.

Combat is lethal, but sane. The rules reward armor and big weapons.

All lab work uses the same mechanic, making it far easier to conceptualize what one is doing in the lab.

To summarize: 5th is more refined and an excellent revision to 4th. It streamlines and "balances" (not in terms of nerfing, per se, but a rationalization of equivalent power). It's quite feasable to port over a 4th edition game to 5th without any real prep. It would not require any significant editing of the world like a 3rd to 4th would have.