Definitely invest in a CPU. The reason being that any GPU beyond the 7850 wouldn't see too heavy of a benefit due to bottlenecking and the fact that the 7850 is fairly powerful to be able to run everything now at 1080p.
Upgrade your CPU / platform now and in the future when GPU's are significantly faster and more power is required to run games upgrade GPU
Tried overclocking the FX? They can reach 5.0ghz if you're lucky, and it'll save you a fair bit of cash, it's gonna be £200 ($300) at least for an i5 setup, and that is for a multiplier locked low-end i5 with a cheap motherboard.
I agree with a lot of the guys in here. You should upgrade your CPU when steamroller launches, it could take a while, but it would prove to give you more performance for your money. When it launches you have probably also saved enough money for a new GPU, so you could upgrade both. Either upgrading CPU now or GPU wouldn't prove to give you a huge noticeable increase of framerates in games. Only if you were to upgrade both.
You could maybe do a slight upgrade on the CPU if you're eager to upgrade right away. FX 6300 is priced around 130$ and you might get lucky and sell your current CPU for 60-70$, by doing so you could get a cheap upgrade, that would let you squeeze some more GPU power out of the system. So you could move a little up the GPU hierarchy.