The two games are very different, despite sharing the same underpinnings. I know plenty of people who played previous editions who don't like 4e, and I know plenty of people who played previous editions who loved 4e. Hopefully we can navigate these rocky, contentious waters without flames.
First off, 4e is fairly light on non-combat rules. This doesn't mean that 4e games are all about combat; it means that the rules assume that a lot of the roleplaying activities that were codified in 3e will be done via freeform roleplay. For example, there aren't any crafting rules for anything other than magic items. There also aren't any general professional skills, and there aren't any NPC classes. If you prefer to have rules for that sort of thing, 3e will be a better choice for you.
Second, 4e uses a power-based design methodology. Classes can be thought of as collections of powers; the differences between classes are defined by the different power choices they have. This makes for a very modular and flexible system. Some people find that it makes the classes overly homogeneous; some people like it.
Third, every 4e class uses powers. That's implied by my second point but it's worth mentioning specifically. A character begins with two at-will powers, that he can use whenever he wants; one encounter power, that can be used once per fight; and one daily power, that can be used once per day. Even martial characters, such as warriors, use this paradigm -- although their "powers" might be better thought of as something akin to a martial arts kata. This was intended to make combat more interesting for (say) fighters, in comparison to the earlier model where fighters just tended to hit things over and over again. If you didn't mind that model, this change may be unnecessary for your play style.
Fourth, 4e leans more heavily on the battlemap. My impression is that the large number of movement-oriented powers both make the battlemap more important and make combat more fluid, but that's definitely a subjective opinion on my part: consider it something to think about if you try 4e rather than a definite fact.
Fifth, 4e introduces the concepts of roles. Roles are a way of classifying classes by what they tend to do in combat. You've got leaders, who heal. There are more of them than just the cleric; for example, the bard is also a leader. You've got defenders, who control the battlefield by encouraging enemies to focus their attacks on them. The fighter is a defender; so is the paladin. You've got controllers, who are somewhat difficult to define, but you can think of them as the classes that affect the flow of a fight: they can hamper enemies, reshape terrain, and so on. The wizard is a classic controller. And, finally, you've got strikers, who purely focus on doing damage. The ranger and the sorcerer are strikers. Every class is primarily one role, but every class has the ability to take on aspects of another role, depending on what the player wants to do.
Sixth, multiclassing is more limited than in 3e. You can multiclass in a couple of ways, but you don't get the same ability to take six or seven classes/prestige classes during the course of your career. 4e classes are fairly flexible, but you don't get the same complete freedom you would with 3e multiclassing.
Seventh, the scope and feel of 4e can be somewhat more epic; or, to put it differently, more broad. The highest level is level 30, and that's very epic play, with abilities that allow characters to come back from the dead. Even at level 1, your characters are significantly more durable than third edition characters, and they'll be able to pull off some really wild things.
I think that hits most of the major differences. It's good to remember that it's still a heroic fantasy game in which characters fight monsters. It still uses a 20 sided die. Also, if you want to try it out, WotC has a free Quick Start kit available.
Alternatively, the new Essentials Red Box will be out in a few weeks; at $20 US, it might be a good way to take a peek at the game and decide if you like it. The Essentials core books will present a bunch of new class variants that change some of the things above: e.g., fighters won't have the same power structure I mentioned. So that might be a better entrance point.
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
In OD&D high level characters had more hit points, a improved to-hit chance, and due to acquisition of magic items, a superior armor class. Wizards and clerics had increased damage due to higher levels spell but all the other classes had flat damage curve. If it increased it was solely due to having a magic item. The difference between the highest and lowest values was not dramatic in OD&D. High level character could be overwhelmed through attrition.
Starting with AD&D 1st, the difference between the highest level and the lowest level began to increase. Non-wizards, particularly fighters, also improved how in much damage they did as well as enjoyed a improved armor class, more hit points, etc.
With 3rd edition the wealth of options increased dramatically for all classes. A trend that was continued in 4th editions. This was especially telling in the use of the open ended ascending AC. Both editions made it easy to push the armor class of high levels to point where a natural 20 was needed by most lower level creatures. Given the fact that the methods of dealing damage increased both in frequency and amount dealt this one-two punch meant that not even attrition tactics were effective against the highest levels.
The open ended scale was also applied to skills and other non-combat skills. Leaving higher level characters with bonuses larger than the +19 difference generated by opposing d20 rolls. This also led to effect where the difficulty of mundane objects became trivial high level characters. Leading to many authors to develop special variant of doors, traps, in the quest to find challenges for high level character. These variants were considered by some to push the limits of being believable.
D&D 5e in contrast caps the open ended bonuses of previous editions. An example is the proficiency bonus which starts at +2 at 1st level and +6 at 20th. Ability scores at capped at 20 when a character levels and gains a attribute increase. Monster to hit bonus and Armor Class are similarly scaled.
This result in a game in which the power balance is similar to that of the 1974 edition of OD&D. Although it is achieved by using a different set of mechanics and numbers.
Character differences The mechanics of the 1974 edition of OD&D were very minimalist compared to later editions. When players attempted as their characters to deal with traps, roleplay with NPCs, figure out mechanism. They had to use their own skills in conjunction with the referee rulings. The implication of this is that in terms of mechanics there was little that was different between characters.
This extended partially into combat where all classes started out with the same to hit chances and dealt the same damage (1d6) regardless of weapon.
AD&D 1st, and 2nd edition made the classes very different from one another. 3rd edition refined the flexibility introduced in 2nd edition so that just about any type of character could be produced throughout the 20th level of play. However this was achieved through the combination of combined specialized elements from classes and feats. Feats and classes themselves were highly specific. A pure fighter was very different than a pure Wizard.
The difference between the characters in 5e returns D&D to a situation similar to that of 1974 OD&D. However unlike the minimalist OD&D, the differences between characters are baked into the mechanics through bounded accuracy.
It can be basically summed up as Any character can attempt any actions but some are better than other at certain actions. A handful of abilities (like spellcasting, martial skill, religion, etc) remain the specialized ability of a specific class. Everything else, anybody can do.
In OD&D the everything else boiled down to player skill. In D&D 5e adds specific mechanics that can be improved through advancement. In the D&D 5e Basic Set this is mostly due to the choice of proficient skills and what ability gets increased. This produced a dynamic that is unique to 5e.