OP, you talked about finance. This is when I get serious, and think you should pretty much ignore everything said in this thread regarding any upgrades except your CPU. Buy within your means. Your motherboard has support for the 8350, and it will provide what the CPU needs. It will run at 4Ghz on that board without any problems, and it will render faster than the 960, and play games faster than the 960. It will make you proud, it will server your purpose in your current situation, and I can pretty much guarantee, as long as you don't play Total War games, you'll be sat on very good average FPS above or around 60.
Yes Intel is faster at gaming
Yes it has lower power draw (but this arguement is total BS, because the price difference in electricity is about ÂŁ10-20/year, so people can shove that arguement elsewhere)
Point is, you're buying on finance. For this reason alone, just buy an 8320 or an 8350, and you will be happy. I could quite happily remove my 780 from my 4670 system, drop it into the 8350 that's sat next to it, and notice almost no difference at all. I'm pretty neutral when it comes to Intel and AMD processors, but in light of the information in this thread, I see the Intel choice being a foolish idea.