with those specs you posted, I say go for the 360. I'm a PC Gamer myself, but I personally would not recommend it unless you're willing to commit to upper tier right components right now. Yes, $500 builds are viable, but with a Radeon 6670? You'd barely get 30 fps on Metro 2033, let alone Crysis 1. True, you can cut out DX11, lower the resolution and texture quality, disable anti-aliasing, and then what? You'd end up with XBox360-level graphics.
On the other hand, if you plan on MMORPGing, or play Team Fortress 2, those specs would be sufficient.