The best you could hope for from AMD is an upgrade that takes your passmark single thread score up from around 1200 (stock fx-8120) to 1600 (4.3GHz fx-8350). That would be a notable upgrade, since the single thread performance is clearly the bottleneck and bane of AMD processors. But keep in mind that a stock 4690K has a passmark single thread score of nearly 2300. And my el cheapo G3258 has a passmark single thread score of 2500.
Well to be fair, that pentium must be overclocked, right?
Never thought I would say this, but I agree with Aten Ra on this one. First thing to do would be to try to overclock the 8120. If the OP can get it to 4ghz or higher, an upgrade is probably not worth it. I think Vishera is only about 15% or less faster per clock than BD, a fair part of the increased performance of the stock 8350 is from increased clockspeed.
If the 8120 will get to 4ghz, it will be within about 10% of a reasonable overclock of the 8350, so with the increased ipc, you would be looking at 20 to 25 percent improvement.
Both at stock, depending on turbo behavior and number of cores used, you could see a larger improvement. No matter what though the FX is going to trail badly in highly single threaded games.