To resolve the debates regarding performance of 7870 vs 580, see the following:
http://www.techpowerup.com/reviews/NVIDIA/GeForce_GTX_680/27.html
580 is 6.5% faster than 7870 at OP resolution of 1680x1050.
Caveats: the 7870 MIGHT overclock better. Also, as the drivers mature for the 7870, the performance gap could narrow. It is safe to assume the 580 drivers are not going to do much to improve its performance at this point given how mature they are.
In any case, not a big difference in performance, slight edge to the 580. But certain games you are playing might favor one or the other.