I'm very familiar with 3.5, somewhat familiar with PF, but only know the core ruleset of 4e. Nevertheless, since no one else has answered, I thought I might as well take a stab at the major differences. I'd say the general theme is that PF offers more paths while building a character, at the cost of offering more dead ends as well. Similarly, monsters are more flexible, but more difficult for the DM to run.
I think you could write an interesting essay talking more about the philosophical and design differences between the two systems, but in answering this question it'll be more useful to address the observable differences point by point.
Class and monster roles
Fourth edition (4e) has clearly defined class and monster roles. This isn't the case at all in Pathfinder (PF). A fighter in PF might be good at dealing damage (striker) or a great tank (defender) but this will depend entirely on how you build your character. Monsters do not provide an obvious indication of how they should be used; the DM has to examine their abilities and think about what their role should be in battle.
It's very easy to build an ineffective character in PF, as a consequence of the greater flexibility you have in defining your role.
Multiclassing
Since in PF each class defines its own progression, every time a PC gains a level they can choose what class to advance in. Again, this means it is possible to design a character that performs very poorly. It would be a bit like creating a 4e character that drew from multiple classes, but was capable of using only heroic level powers while everyone else was choosing a paragon path.
Paths vs. Prestige Classes
In 4e, there are three distinct tiers of play, and you can choose a paragon path and epic destiny as you progress.
There's no direct analogue to the tiers in PF. The closest thing to a paragon path is a prestige class -- a class that can only be taken when you meet certain requirements. This was more of a big deal in 3.5, where it was used for character customization; in PF there are many fewer prestige classes, though they might be important for certain multiclass combinations.
Defenses v. Saves
This is purely technical, but confusing if you're not expecting it. Defenses in 4e are equivalent to saving throws in PF. If a wizard casts a spell, rather than rolling an attack, the defender rolls a saving throw against a DC set by the spell.
Automatic progressions
In 4e, you add half your level to a great many statistics. PF is not quite so straightforward -- your class(es) will determine your base attack bonus and saving throw progression, and you must pick how your skills improve every level. Other abilities like AC or initiative do not naturally increase as you level.
Powers, Spells, and Maneuvers
This is probably the most fundamental difference from a player's perspective.
In 4e, every class has a list of powers they can learn as they level. These powers are divided into at-will, daily, and encounter powers that dictate how often they can be used. Pretty much any special ability a player has is derived from a power -- and those powers are chiefly geared towards combat. Casting classes can gain rituals which are less combat related, and work off a different economy than combat powers.
In Pathfinder, it works a little differently. Casting classes have spells, which are probably closest in spirit to 4e powers, but tend to be more flexible. The number of spells you can choose from is quite large, and different classes have different mechanics for learning and casting these spells. Spells useful in combat consume exactly the same resources as more role-playing oriented spells.
Meanwhile, melee classes rarely have the same type of limited powers. Anyone can push, grab, pull, grapple, trip or disarm a foe during combat, and you can do so as often as you like. Doing so means sacrificing damage, though; you will only do damage with a regular attack. Unlike 4e, forced movement is quite difficult to pull off in PF, which is why a grid isn't as necessary.
As an example, a fighter in PF progresses chiefly because they get better at what they've been capable of doing all along, rather than getting spectacular new powers.
Monsters
This is a big difference from the DM's POV especially.
In addition to fitting certain roles (as mentioned above) monsters in 4e are often defined by a set of bespoke abilities. In contrast, monsters in PF always play by the same rules as the players. Their hp, attacks, saves, and skills are defined and limited by the type and HD of the monster. The majority of unique special abilities are copies of spells, or one of a small set of abilities common to many monsters. Often a powerful monster will have a large set of abilities they will never use in combat, but can provide role playing hooks.
There is no PF equivalent to elite or solo monsters -- you simply must use a higher level beast to provide a greater challenge to the party.
Overall the 4e system is much easier on the DM in creating encounters. For those so inclined, though, the PF system allows the creation of some interesting beasts; you can even add class levels to monsters, much like PCs can multiclass.
Magic items
The majority of magic items in PF do one of two things -- they either increase the attributes of a PC, or they can replicate the effects of spells. Magic weapons and armor combine several different attributes, almost Diablo style. Compared to the 4e items in core, they are much more varied, and what specific item your character has can drastically affect what they can do. The downside is that it becomes harder for a player to choose the 'correct' gear.
Best Answer
The developers have previewed us with the major system differences on this blog article:
Hit Points, Stamina Points, and Resolve Points. In Starfinder, Hit Points measure the health and robustness of a character, while Stamina Points measure a character's readiness and energy (and can be replenished far more easily). Whenever you take damage, your Stamina Points are depleted before your Hit Points. In other words, you can soak up some hits without too much trouble, but once you start taking damage to your Hit Points, you're taking physical wounds that are much harder to heal quickly.
Starfinder characters also get a third pool of points called Resolve Points, which represent grit and luck. You can spend Resolve Points to power (or enhance) some class features, or to help you stay in a fight longer. Resolve Points also determine whether or not you die if both your Stamina Points and Hit Points are reduced to zero.
You can recover all of your Stamina Points by resting for 10 minutes and spending 1 Resolve Point; Resolve Points and some Hit Points are replenished after an 8-hour rest.
Armor Classes. Characters in Starfinder have two Armor Classes: Energy Armor Class (EAC) and Kinetic Armor Class (KAC). Attacks that deal energy damage (like the fire damage from your trusty red star plasma pistol) target EAC; attacks that deal kinetic damage (like the bludgeoning damage from a gravity well hammer) target KAC. Starfinder has no flat-footed or touch AC.
No Iterative Attacks. Starfinder characters normally get a single attack every round, and this holds true from level 1 to level 20—a character's number of attacks does not increase as their base attack bonus goes up. Instead, any character (even at first level!) can use a full action to make two attacks in a round, each at a -4 penalty.
Attacks of Opportunity. In Starfinder, only three things provoke attacks of opportunity: moving out of a threatened square, making a ranged attack, and casting a spell. That's it. No other actions provoke attacks of opportunity.
Magic is Magic. There is no distinction between types of magic in Starfinder, whether arcane, divine, psychic, or something else. Spellcasting classes like the mystic and technomancer have different spell lists, but are both harnessing the same latent magical energy that permeates the universe. In addition, spells in Starfinder have no components; all you need is the ability to cast a spell and concentration.
But there are way more changes in the system, some subtle, others not so much:
Character Creation
Point-buy. The points are now worth 1-to-1, meaning that the same point could raise an ability score from 10 to 11 and 15 to 16.
Traits. The system was replaced by the Themes, which are similar to D&D 5th edition Backgrounds, but give you an ability bonus at first level an knowledge-related ability specific to each theme, and bonus abilities at higher levels (at 6th, 12th and 18th levels). Themes can be used with every race and class combinations, and will never replace class features.
Archetypes. The idea for archetypes is that you can take archetypes with more than one class now, and depending on your class, the archetype will replace different abilities. There is only one archetype in the book, so we will have to wait to see how this plays out later on.
No classes grant 2 skill ranks per level anymore, they want skills to be more useful throughout the game.
Ability Scores gain a bonus every 5 levels now (down from 4). But the rule has changed, if the ability score is equal or bellow 16, you gain a +2 increase. If it's 17 or higher, it increases by +1. And you gain four increases on four different abilities of your choice.
Equipment
Carrying Capacity. Tracking the weight of carried gear is no longer an issue, characters have a limit on what they can carry called Bulk, which is half your strength score, and each bulky item consumes a certain amount of bulk. A regular backpack increases your bulk as if your strenght was 1 point higher, and a military one increases it as if your strenght was 2 points higher. Though they cost 1 bulk, they don't cost any bulk when properly worn, only carried.
Critical Hits changed drastically on weapons. They only crit on a natural 20 (unless you have an ability saying otherwise, like soldiers), and they always deal double damage. But a lot of weapons have a special effect on a critical hit, such as causing the target to bleed, or cause extra fire damage, or even cause the staggered condition. A confirmation is no longer necessary for natural 20, but other results like a 19 on a 19-20 attack would require confirmation.
Skills
More skills are condensed into others. Like, Athletics now has rules for swimming and jumping, while Acrobatics has the rules for balance, tumbling, flying, and escape grapples and restraints. Handle Animal and Ride got condensed inside Survival, but there are no rules for tricks and training, you simply use the Diplomacy mechanics with animals using Survival.
Use Magic Device is gone, but scrolls and wands still technically exist, they are much less common now in a setting where anyone can buy a flamethrower and jetpacks.
Profession. The skill changed significantly, but the major change is that it now uses any of the three mental stats as base (int, wis or cha), and you get to pick which one if no example is provided.
Craft. It is much easier now to craft something you cannot find on shops, and takes much less time. You spend a certain amount of credit (equal to the market price of the item) and after a certain amount of time, based on the level of the item, it is done. Each item has a level, which decides the necessary ranks in the crafting skill you must have in order to create it. Selling anything crafted by yourself will result in 10% of the market value though. Crafting feats (magical or mundane) are nowhere to be found.
Diplomacy. The skill is still used for the same things, but the DC has changed significantly, it now works similarly to Intimidate, the DC is 10 + 1-1/2 the target CR (CR 4 creature is DC 16) or 10 + his total diplomacy (+5 diplomacy check results in DC 15). The skill clarifies that the target must have 3+ int, speak the same language and that it takes at least 1 minute of interaction. The initial attitude affects the DC (hostile +10, unfriendly +5, friendly -5).
Heal is now known as Medicine (for obvious reasons) and uses intelligence as base ability. The DC for long-term care is now 30 (down from 15, but a medpatch can grant +10 on this check and be used untrained) and still works pretty much the same, but if you exceed the DC by 10 points, they recover three times as many hit points and ability damage. The effects of Treat Deadly Wounds have changed, it takes 1 minute instead of 10 minutes, and now you can treat it twice per day if a medibay is used (up from once per day), and the DC is based on the equipment being used (25 for a medkit, 20 for an advanced medkit). There is a feat called Medical Expert that allows you to treat deadly wounds as a full round action using a medpatch.
Combat
5-foot step is gone as we know it. We have an move action called Guarded Step, which allows you to move more carefully for 5 feet. If you gain bonus move actions, you could also use those actions to make extra Guarded Steps.
Conditions. While the game has the exact same conditions from Pathfinder, their effects have changed. The flat-footed condition, for instance, happens if you have not acted in combat yet and you simply take -2 to AC.
Haste and effects that would grant additional attacks simply means the penalties are reduced if you decide to make multiple attacks that round. Autofire weapons allow you to make a single attack roll and affect multiple creatures in an area if your result is enough to hit their AC, like an area spell (source).
Swift Actions. Changing your grip on your weapon and dropping prone are now swift actions, and you only got one swift action per round, but you can downgrade a move action to a swift action. Reactions (known previously as Immediate Actions) and Swift Actions are completely separated from each other.
Reactions happen after the action that triggered them, unless they are a defensive reaction (like Total Defense), then it happens before the trigger. This is a new type of action to cover several situations. Attacks of opportunity are now Reactions and still happen before the action that triggered them.
Precise Shot. The -4 penalty for firing with allies within 10 feet of your target is gone, along with the feat that removes said penalty. The aiming systems of all weaponry are simply superior.
Combat Maneuvers are all Standard Actions, even sunder, trip or disarm. And you can pin a target that you attempt to grapple and exceed his kinetic AC by 13 points. CMB and CMB are gone, and each maneuver must be checked against the target's kinetic AC plus 8. Feats are no longer necessary as no maneuver causes attacks of opportunity.
Difficult Terrain and Hampered Movement. If your character's movement is doubled twice, then each square moved counts as 4 squares (6 on diagonals). If it is doubled three times, then each square counts as 8 squares (12 on diagonals).
Magic
Areas and spell terms are now separated from the magic chapter, including descriptors and rules commonly used by spells, such as Charm, Concentration, Instantaneous, Line of Sight, Cone areas, etc
Concentration checks are gone (source). But some spells still require concentrating on their effects.
Prepared spells are nowhere to be seen, both casters presented in the book are spontaneous casters (spells knows and spells per day mechanics).
Spell levels, spells are condensed between 1 and 6 spell levels, certain spells that are 9th level spells in pathfinder are 6th level spells in starfinder.
Touch spells mostly do not allow attacks of opportunity against you. There are other spells with this exception, but each individual spell calls this out.