Intel Pentium G3258 vs. Intel i3-2120

No I dont think its worth it IMO.
You will lose hyperthreading (HT), 100Mhgz speed (easily regained with overclocking), and Drop from HD2000 graphics to HD. Both have quicksync.

HT makes up for the 10-20% core improvement going from SB to Haswell so the only real 'gain' is the ability to overclock. If thats what you're looking for then this would be the cheapest route to go.