The performance between the 570 and 6970 is fairly minor. My personal prefrence is Nvidia cards so id be leaning towards the 570, however neither will disapoint.
For the 6970:
550 Watt or greater power supply with one 150W 8-pin PCI Express® power connector and one 75W 6-pin PCI Express® power connector recommended
For the GTX 570:
Minimum Recommended System Power 550 W
^ Information taken from manufacturers website.
So yes, any good 600w Power Supply would be perfect.
Leading brands; Corsair, Antec, XFX, OCZ are a few to look at.