Just a random thought that's been percolating in my brain recently. It's no where near developed fully, but I figure I might as well throw the first draft out there.
One reason that different versions of D&D "feel" different is the metagame that goes on behind the actual play. Different versions seem to encourage different metagame focuses that run parallel to the actual game play. Here's my initial ideas about what some of the editions encourage for "metagame play"
OD&D/Classic D&D/1E AD&D: Using player ingenuity to make the most of what the random rolls give you at character creation, and what random shit the DM gives you in play. It's a little beyond simple resource management on a strategic/tactical split. It's really about coming up with that odd idea that makes an encounter easy (or at least easier).
2E D&D: Making your character so interesting and fleshed out that the DM grants you plot immunity. This is not knocking the game. 2E focused on the grand plots, and clever ideas and all that are nice, but making the DM think twice about letting you fail that save vs. petrification counts more when the plot is on the line.
3E/Pathfinder: Optimizing your character build. When I say optimizing here, it's not necessarily about DPS (to borrow the MMO term), it's about finding the right mix of ability scores, classes, feats and skills to craft the "perfect" character for whatever it is you want to do in the game.
4E: Optimizing your adventuring party. 4E really plays up the "tactical war game" aspect of D&D. Making sure you've got not only a competent character, but that your character fits into the overall makeup of the party seems crucial to successful 4E play. Fail to "play your role" and those big long encounters can become bigger and longer.
Now, like I say, this is just my initial ideas here. I'm not trying to knock any play style, just thinking in print about what makes the play of each edition different. If you've got comments, criticisms, or can think of anything I'm being just plain stupid about, feel free to let me know.