What resolution are you playing at? That FX will choke off a few frames but if you're at 1920x1080 it wont really matter because a pair of GTX570's will be giving you more than 60 fps in every game so you wont see a difference.
If you're at 2560x1600 or higher, you're gonna want some more CPU muscle so yes, a 8120 will be a proper upgrade. You'll also want to invest in some good cooling because you'll need to overclock that 8120 good and proper like 4.5 or so.
A 8120 with something like a Noctua D14, running 4.5 GHz, will give you very nice performance.