Hello! While the AMD FX-8120 is a decent processor for heavily-threaded applications, it is actually slower than the Intel i3 (any Sandy/Ivy Bridge Intel works here) on single or lightly-threaded applications such as gaming and general use. View the benchmarks here:
While cpubenchmark.net does provide some comparison, it doesn't provide benchmarks, which is really what you want to look at.
Since you said you are a PC gamer, I would definitely recommend the i3-3220 over the AMD FX-8120. Since most games do not make use of more than 2 cores (some using 4) the FX-8120 will actually give you worse frame rates (as seen in the benchmarks linked above).
Now I'm not 100% sure how the price differs between where we live, but from just doing a currency converting app it seems you have about $190. This is enough for an even stronger processor, and Intel i5 Sandy/Ivy Bridge. If you can afford it, any Intel Sandy or Ivy Bridge i5 will give the best gaming performance (and performance/price ratio) of any current processor.
Final thoughts: If you have the bank for it, get an i5, if not, stick with an i3. Good luck!