Check out the amd fx 8350. It even beats out the 3770k in a lot of aspects, and its only $160-180. With 8 cores it would dominate for streaming. Also, switch out the 650 for a 7850 or 7770 (or something amd, maybe you could find a 7870 for cheap).
650w is overkill, but go with a quality psu. Most important part of the build, plus a good seasonic will last you forever.
Also, with a 8350 you need a good motherboard. Don't go with a $50 mobo with a $150 cpu, its going to blow up haha.
do you live near a micro center? They have sick deals for the 8320/8320.
But otherwise, pick up a 990 mobo, either the gigabyte ud3, the asus M5A99FX PRO R2.0 or the asrock extreme 4.
http://teksyndicate.com/videos/amd-fx-8350-vs-intel-3570k-vs-3770k-vs-3820-gaming-and-xsplit-streaming-benchmarks - good benchmark of them