I dont think there is any 'real world' difference between playing BF3 (and other DX10/DX11 games for that matter) on either Vista or Win7. If there was a difference it would be a game specific compatibility issue. BF3 runs smooth as silk on my Vista 64bit.
The only difference to consider is if your Vista or Win7 is 64bit or 32bit. Obviously 64bit is the better choice, but again if you had a 32bit version, you probably wouldnt see any difference or negative effects on gaming performance.
The only difference to consider is if your Vista or Win7 is 64bit or 32bit. Obviously 64bit is the better choice, but again if you had a 32bit version, you probably wouldnt see any difference or negative effects on gaming performance.