I think I'll just touch on a few of what I think to be the significant differences between 3e and 4e:
1. Diverse vs. similar power structure for characters: 3e classes tended to have a mix of abilities: some classes had abilities that could be used mostly at-will while others (mostly the spellcasters) had abilities with daily limits. 4e classes tend to have the same power structure: a small number of at-will powers (two to four so far, depending on race and class), a small number of encounter powers (abilities that are refreshed after a short 5-minute rest) and a small number of daily powers (abilities that are refreshed after an extended 6-hour rest). In addition, 3e characters (especially 3e spellcasters) had more scope to select abilities that were primarily useful out of combat. 4e characters have less scope to do so: the majority of their abilities are specifically "attack" or combat powers, and a smaller number are "utility" powers which could have either combat or non-combat applications.
2. Daily balance vs. encounter balance: Because 3e had characters with daily limits to their abilities, 3e was primarily balanced over an adventuring day. Such characters would start out quite powerful and flexible, and gradually lose power and flexibility as they used their daily powers, until it was no longer feasible for them (and presumably, for the party as well) to continue adventuring further that day. Conversely, 4e is primarily balanced over an encounter. While daily abilities are certainly useful, they do not form the bulk of any character's abilities. A party which is completely out of daily abilities is still able to take on reasonably tough challenges. In addition, certain abilities such as action points and most healing powers can normally be accessed only a limited number of times per encounter. This sets some limit on the amount of power or endurance that a character has at his disposal in any one encounter.
3. External vs. internal healing: In 3e, healing tended to come from an external, usually magical source: a spell, a potion, a wand, etc. In 4e, healing mostly draws on the internal resources of the character: even external sources of healing such as clerical healing powers or healing potions usually require the character to expend his internal sources of healing (called healing surges) to benefit from them. Even without external sources of healing, a 4e character can recover hit points by taking a short 5-minute rest and expending healing surges. This has caused problems for some players and DMs who have been used to tying hit point loss to physical injury. Others have argued that 4e hit points represent more intangible aspects of a character such as skill, stamina, luck, divine favor, determination, etc. and the non-magical recovery of hit points represents the replenishment of these intangible aspects without healing physical wounds. Such non-magical "healing" thus does not cause physical wounds to disappear, but allows a character to fight on despite his wounds.
4. Process vs. outcome: 3e tends to define abilities in terms of process. In order for a fighter to pull an opponent towards him, he might have to use a harpoon or a lasso, throw it at an opponent, and then succeed on a Strength check. 4e tends to define abilities in terms of outcome. Come and get it, a fighter encounter power, allows the character to pull nearby opponents adjacent to him, but does not specify how he does so. It is up to the player to describe it, and he need not use the same description each time: perhaps in one fight he taunts his enemies. Perhaps in another he bluffs them by feigning weakness or an opening in his defences. He might also lasso them, or pull a rug which his enemies are standing on. This has caused problems for some players and DMs who are more used to consistency of processes and outcomes.
5. "Martial" does not mean "ordinary": In 3e, martial characters were usually limited to feats that could be accomplished by a sufficiently skilled or lucky ordinary man. 4e raises the bar of what can be accomplished by martial characters, to mythical or fantastic levels. A warlord (a martial class with abilities similar to the divine cleric) can inspire a dying comrade (at 0 hp or less, but not yet dead) so much that he regains hit points, stands up and starts fighting again. A fighter with come and get it can reliably cause an enemy archer or wizard to move next to him in combat. A halfling rogue with a dagger can attack a Gargantuan creature and knock it prone. Again, some players and DMs find this difficult to accept.
