Advice for computer upgrade!

[tools4fools]

GRAthos,

you seem to have some good knowledge about graphic cards. I'm getting a new PC myself and am a bit confused when it comes to graphic requirements. From reading up here I'm down to a few cards:
Cheaper:
Gainward GTX-560 Ti Phantom 2GB GDDR5, PCI-E 2.0 x16, HDMI
more dosh:
Sapphire HD 7950 Dual Fan 3GB, PCI-E x16 3.0, DP, HDMI
even more:
ZOTAC GTX-580 3GB DDR5, PCI-E 2.0 x16

Question is:
Will the game be smooth on high settings on a 560 Ti or is one of the other cards required for this?
Is 580 much better than 7950, if yes in what way?

Rest of setup should be fine, SSD, i7, 16 GB ram, some Samsung 24" screen.

Thanks for any info.