There will be nearly no difference at all. See if you can get an i5 2500k or i5 2400.
both i3's have the same clock speed. go with an i5 or i7 if you want a noticeable difference.
Your i3-2120 has a passmark rating of 3874 when all 4 threads are in use. The single thread rating is 1684.
The i3-3220 has a better architecture, resulting in a total rating of 4209, and a single thread rating of 1761. Really, not a big jump.
Particularly for games which need the performance of the single master core.
Regards 😉