they are in the same performance ballpark with the 7870 being the newer card on the market (and more efficient if your PSU is an issue). check several reviews (like the link) and see which card performs better in games you like to play.
For some reason my old 570 would get more stuttering/input lag than my 680 in bf3 at settings with very high fps. It wasn't the difference in fps I was noticing... I think it was the 1.25gb vram that was causing it, I would go 7870 for the 2gb of vram.