The 7870 starts around $350 but right now and at the same time the gtx 570 is dropping into the 270-290 range after rebates which IMO justifies the purchase of the older card at this moment.
7850 is better than a 570
I wouldn't go as far as saying that the 7850 is better than the 570. They both offer similar performance, however like someone said before you're getting power efficiency and more VRAM with the AMD card
At similar price points, the 7870 is the better choice. If you can get the GTX570 on the cheap, then it could be an option. Also, the GTX570 is a good card up to 1920x1200 resolution. Above that, the 1.28GB memory will be a limiting factor.