Performance wise, between those two cards, is going to be decided by what games you play (it's critical when choosing between these cards some games really prefer one arch over the other) and features you want. The two cards have nothing to really separate them in general gaming power.
Some will tell you to get the 6970 if you are running 2560*1600 or higher and the 570 for below that. Makes little sense to me, since if a card can run a game acceptably @ 2560*1600 or higher it can run it at lower res too. I understand there will sometimes be a few FPS more at 1920*1080 with the 570, but those FPS will be superfluous, anyway.
The 6970 has more RAM (for me this is the single biggest difference), can run single card eyefinity, and is more power efficient, if that matters to you, and the 570 has CUDA and PhysX, if that matters to you. Other than that, if you have no brand preference and they aren't separated by the games you play, flip a coin.