I've recently had the exact same dilemma (well, and the gtx 1060, but that plan went out the window quickly).
I've gone with the 580 after seeing loads of benchmarks. I'm gaming on 1080p @ 60hz, and the 570 seemed to struggle to get around 60fps in most games. While the 580 was ten to fifteen frames ahead, which is a huge difference. Especially if you want it to be a bit future proof for the next couple of years.
So I chipped in some extra cash and got the 580.
8 gig.