(resurrecting the dead).
Mostly good advice, but it really depends on the game. A lot of developers are going with crappy console ports these days, which actually suffer with less than 4GB of VRAM, even at 1080p. Obviously, that gets more apparent with older 1GB cards, and as you bump the resolution past 1080p, move to a 144Hz display, or both.
In the meantime, if don't mind cranking down the AA and other settings, you can by most games with a 7970 just fine.