Only Battlefield 2 benefits from 2 GB ... and that's not because the game has a very complex engine, but mainly because it's simply a system resources hog due to the way it was coded.
I mean, compare BF 2's engine to say ... Source engine. Play BF 2 and Half-Life 2 for one hour, and tell me which one lets you come back to the Desktop without your HDD working like hell.
That game (BF 2) stutters even on my system. It's always happening at just when the map loading is completed, and I enter the game.
It stutters like no tommorow for at least two or three minutes, and it eventually stops to let super-smooth gameplay, and frame rate never drops too low. No lag either.
And when I come back to the Desktop after playing it for say ... 30 minutes, I immediately open the Task Manager, and look at BF 2's .exe and see how much RAM it takes. Usually it takes about 860 MB, and lowers itself to eventually terminate itself (the process). While the .exe is preparing to terminate, the HDD works to a point where my Desktop reacts to everything extremely slowly.
Even F.E.A.R. is much smoother than that, and never slaugther my Desktop "performance" like that when I quit it. Same goes with H-L ² or Doom 3 or UT 2004. Or any other games I own.