I would not do that. AMD is about to launch it's new processor lineup which apparently will finally be competitive again when compared to Intel's CPUs. I would stick with what you got and wait to see how the new AMD CPUs perform. If they don't meet your expectations I would consider switching to Intel. You will need a new mainboard nonetheless since AMDs new CPU generation will be based on a new socket. At least that's what I'm doing right now.
But if you want something more sophisticated right now you will have to switch to Intel CPUs. If you do that a new upper-class GPU will make sense. Or you could indeed get a AMD FX-8350, they are pretty cheap to get. But this would still not justify a high powered graphics card. And my...