Assuming you want to play games with this build or even run daily apps:
Check out my $650 build here:http://www.squidoo.com/electronicandmore#module146695821
You get a better GPU, better monitor, and CPU for a lower cost.
The FX-6300 with a 7870 will game better than the i3 3220 and a 7850 hands down. The FX-6300 can multi-thread better anyways, but whats most important is the GPU is better. In most games at 1080P, the most important thing to them is the GPU if it is demanding like BF3 or Metro 2033, even Borderlands 2 doesn't have effects of CPU difference:
Metro 2033: http://www.overclockersclub.com/reviews/amd_fx8350/8.htm
You don't need a sound card or Windows Pro either.
It should be noted the FX-6300 can overclock and it's a similar price to the i3 3220. Also, AMD will be keeping AM3+ socket so you'll be able to upgrade for another 2 generations at least with each generation having an expected 10-15% increase in performance like from Bulldozer to Piledriver. And the multi-threading will be noticeable in applications .