Better CPU, just a little less powerfull GPU, but a bit cheaper and CUDA and OpenCL should have similar performance at this level. http://pcpartpicker.com/p/bnFJBm
I'm guessing you will play on 1080p, so even an R9 270 would perform good and the price difference allows the addition of an SSD. http://pcpartpicker.com/p/cHDCCJ
Both builds are a bit over $600, but offer good bang for the buck.
My recommendation notice it has a capture card it will help greatly with your streaming I linked to the newegg site for it though the price i listed is for a used one off Ebay.