For the most part, similarly. There are only a few games that use more than 4 cores and they perform quite evenly. In BF4 for example the i5 quads perform very similarly to the FX 83xx at 1080p I believe. In a game like Crysis 3 though (a very isolated example), the FX 83xx will perform better.
Regardless, with your current video card you won't be seeing great fps in these games. The video card makes the most difference in gaming - you could either go to a 3570k + a new video card, or just get a new video card. Your i3 will perform similarly or better than an FX in single-threaded/lowly threaded games, it is only in a few instances where games use more cores that the FX will outperform it (4 cores and up, most likely).