the i5 3570k a noticeable stop from the i3 2120?

i5 3570k Ivy Bridge Quad Core 3.4GHz
i3 2120 Sandy Bridge Dual Core 3.3GHz + Hyperthreading

I recently built a new pc including the i3 2120, and I noticed that I can't really run all of my games on maximum, although that isn't my problem really, I like to livestream some of my games and when I do that I tend to have to lowet my settings, I make Far Cry 3 have medium quality settings on 1440x700 when recording, if I bought an i5 3570k, would I be able to put some Very High settings while recording?

Also I get approx. 45 FPS in Crysis 2 at 1440x700 + Max Quality Settings with my i3 2120, what FPS would I get around if I bought the i5?

Incase i'm terrible at asking questions,
Is the i5 worth an extra $250 or should I be content with my i3