If you are changing BOTH the CPU and the Motherboard then why not go with an Intel setup?
The i5-4440 is reasonably priced and about 20% faster on average, though it varies between 0% and 40%. Skyrim, for example is about 40% faster on the i5.
The i5-4440 isn't overclockable, you'd need an i5-4670K for that, but very few games currently benefit from overclocking the i5-4440 (but you do need to overclock the FX-8350 in many games or it's a bottleneck).
I've been recommending this combo to several people:http://pcpartpicker.com/part/intel-cpu-bx80646i54440