I'm skipping around a bit, since I thought I'd tackle the two editions of D&D that I've played before I risk the rest of the versions that I'm familiar with mostly by hearsay. More importantly, there are more differences, and more significant differences, between 3rd edition (and its identical for our purposes revision) and its predecessors than between any of the older games. Best to get the broad strokes laid out before diving into minutiae.
Not that the differences between the game I started with and the older versions I'm just now discovering are staggering. It's still got the same basic core activity of every edition of D&D -- kill things, take their stuff, level up. How you get XP is a little different, loot is a little different, and what you get when you level up is quite different, but the outlines remain the same.
The experience system suffers mostly stylistic changes. I'm not well versed enough in the lore of AD&D to know if the business about "overcoming challenges rather than killing monsters" is unique to 3rd Edition, but even if so there's not as big of a difference as you might think. The book does suggest "XP for achieving story goals" and "XP by fiat" as options, and there's some talk in the challenge rating system about adjusting those ratings to take into account the difficulty of the circumstances, but CRs, and the accompanying XP, remain mainly attached to monsters.
Loot -- particularly of the magic variety -- contains some more significant differences. The CR system assumes that the PCs have a certain amount of magical equipment at each level, and magic items can, in a normal campaign, be purchased freely. There's no mention of XP for treasure since gold is now it's own reward, effectively becoming a point buy character generation system tacked on to the existing level based one.
The changes to treasure only foreshadow the really big innovation of third edition: powers. I don't use that word in the 4e sense (though that is where they end up) but rather just as a general term for all the mechanical stuff that PCs in third edition get. Spells, feats, class abilities, skills -- not to mention all the strange new subsystems introduced in books like Magic of Incarnum, Book of Nine Swords, and the Psionics Handbook (and its Expanded descendant).
In many ways, the proliferation of powers is a good fit for the core activity of D&D. It's an addition that most of the video games based on the game have made, and it grows naturally out of spells, and special ability based classes like the monk. It adds a new angle to play -- the character build -- that provides a good "away from the table" activity for players. But mostly it just means that everyone gets a decision or two when they level up, strengthening that particular motivation, and the core activity as a whole.
But it does tend to shift the focus. The proliferation of powers, and associated uniqueness of each character and difficulty in creating new ones, naturally leads to a greater focus on the characters and away from the campaign that contains them. (I suspect that the changes to third edition reflected a pre-existing shift in play style rather than forcing a new one on everyone, but it does have an effect on new players picking up the game.)
Even a dungeon crawl--heck, even if you're using the same dungeon--in third edition will differ significantly from a dungeon crawl in OD&D, due to the changes in the kill/loot/XP/level cycle and to all the little peripheral adjustments in third edition. One game will be about conquering, or being conquered by, the dungeon, and the other will be about the characters doing the conquering. Just because systems share a core activity doesn't mean the games you run with that system will be the same.