Surprisingly enough, I agree with most of what Cerebrim said.
I think that there has also been a corresponding shift in the balance of power away from the DM and toward the player, because so much more of the game rules are focused on customizing the player and so much fewer areas of the game absolutely require DM interpretation.
This is a very common interpretation and I believe it to be somewhat mistaken. Or, rather, only half right. It's very much true that 3e takes power away from the DM. The fact that many of those holes mentioned by T Foster have been filled (or at least an attempt made to fill them) means that the DM has less wiggle room for interpretation.
However, it doesn't give the power to the players. The rules keep the power for themselves. If the rules gave the power to the players, then it would be the players who would adjudicate actions. Previously, if my PC wanted to jump a ditch, it was up to the DM to determine whether or not I could do so. Usually he'd give a saving throw, or perhaps a strength check, or some other (usually) reasonable approximation and away we'd go. The point is, it's the DM who creates the rule in this case. In 3e, I know exactly how far I can jump because the rules tell me so. If I can't jump that distance, there should be some outside force changing the equation.
But, in no case can I, as a player, say that I roll a Reflex save to jump the pit. And, really, the DM is encouraged not to do so either. The rules say you can jump X feet depending on the situation. Neither the DM nor the player have any real power here unless the DM decides to overrule the rules. Which is his prerogative, but, for the most part, I think isn't done very often for any number of reasons.
How do the editions play differently? I honestly think that the differences in my game have far more to do with my growth (or lack thereof) as a gamer than with the edition. My games have varied pretty wildly under each edition with the pendulum of combat and non-combat swinging back and forth. I honestly don't think any edition particularly encourages any particular play style. I've done high intrigue and high hack in all editions.