CryENGINE 3 Loves the AMD Radeon HD 69xx/77xx/78xx/79xx (Cayman/GCN) series, and Nvidia Fermi/Kepler GPUs. The reason? Because once you touch that DX11 button, performance goes up the roof, but so does tessellation. Older cards have issues handling the tessellation. However, in DX9, the GPU isn't used nearly as much as the CPU for whatever reason. It's why I'm able to play it on my quad core Phenom II laptop with integrated 4250 crapics at ~24-30fps. (albeit at minimum settings at 480p.)
The 580 does okay, though it falls behind the Radeon HD 78xx series which seem to be made for CryENGINE almost... see here.

And that is here;
http://www.techpower...HD_7870/13.html using the beta drivers that came with the test cards for TPU.
And here it is with the newest drivers (with the 680 on the block);

(note the 78xx series is missing?)
So you should be fine with your system. (note these are in DX11 with high resolution textures and all settings maxed.)
Edited by Vulpesveritas, 05 May 2012 - 05:13 PM.