I would personally go with the Nvidia GTX 580 because... Nvidia has PhysX, there arcitecture is much better than ATI's (This is really important this is what will get you more FPS in games).
Then 5970 is a dual chip and many games do not support that so you would not get the full potential of the card, but anyways the 580 is much better performance wise is scored much higher than the 5970 in almost all tests.