Dealing with the same question actually. Currently running Eyefinity with a single 5870. What I'm thinking is, if the 570 outperforms the 6970 and is the same price or less, I'll grab a 570 now and another one next month. If the 6970 is the same or better than the 570 for about the same price, I'll go for that, and maybe another next month, but I'll be able to do Eyefinity right off the bat. I kind of want to stay away from SLI/Crossfire configs though, as I read a lot of negativity about microstutter. Maybe that talk is overblown. Not really sure what to do atm, but I want to spend some money tomorrow!
It looks like that are pretty close in performance with the 6970 being a little more expensive. You can't go wrong with either, but I'd go with the GTX570 simply for the folding potential and physx.
This is what I'm going to do. I notice a lot of hitching due to framebuffer in large, open-world games playing at 5760x1080. The 6970 seems to improve in comparison to the 570 as the resolution and features get cranked up. Also, Crossfire scaling was up to 97%(!) in some games, so adding a second card down the road should power through anything in Eyefinity.