Upgrade from HD 6970 to R9 280X?

Get a better cpu like the i5 4460. You don't need 16gb ram, get 8gb at 1600MHz. Upgrade gpu to r9 290. About same budget as you would spend but better performance in gaming.
Edit: Sorry though you are planning to buy an 8350 didn't read it correctly that you already have it.
 
It's somewhat limited in respect to variables, but it does offer a pretty solid baseline using equivalent hardware as at least a basis for comparison. I've been talking with Ryan and Ian over at Anandtech and from what Ian has told me about what they do in the lab as far as testing, the Anandtech bench scores are the result of a seriously thorough process.