Here's a good place to check these things out: http://www.anandtech.com/bench/Product/511?vs=540
(the 5870 is slightly faster in most situations but uses more power; the 560 is basically a tossup with the 6870)
Also note that quantity of VRAM has little effect on the frame rate unless you're talking about high resolution or very high AA settings. 1GB is enough for your typical mid-range card running at 1080p or below. 2GB is better, but that should rarely be the reason that you choose one card over another. In the case of the 7770, it's dramatically less powerful than the other cards, so going to 2GB is irrelevant.