It doesn't go that way, and it depends on the game. And no one can predict what the upcoming games is carrying on, and the 1 GB of VRAM might be an issue for VRAM hungry games such as GTA IV, Crysis 2.
The higher the resolution in games, the more VRAM there should be since more textures need to be loaded. However some cards are not powerful enough to use the extra VRAM.
Due to technologies such as AA, MSAA, AF, QSCAA.. those really feed on the VRAM depending on the game.
Since you'll be gaming @ 1080P the HD 6950s should serve you quite well, at least for the current BF3, Crysis2, Metro 2033. Upcoming ACR, MW3 and some good games.