budget amd wins and not sure how well going to a athlon x4 to a phenom II x4 is for bottlenecking a 660 gtx, but should be better and easiest upgrade as u have a am3 motherboard, if am3+, then an fx piledriver cpu. Intel is best solution with a ASRock Z77 extreme 4/6 being recommended and i5 3570k/2500k, but an i3 will work and usually better than a PII X4.
Intel Socket 1155 will match any sandy bridge or ivy bridge cpu being the 2nd and 3rd gen core i3/i5/i7 series cpus or 2xxx 3xxx model numbers. and ur athlon an am3 will work in an AM3/am3+ motherboard and fx only in AM3+. FX cpus being bulldozer 41xx/6100/6200/6300/81xx cpus piledriver being 4300/6300/83xx cpus on the am3+, and Phenoms II X4/X6 on AM3 and AM3+, saying since u mentioned compatible not sure if u know sockets matching as its kind of self explanatory but some seem to not get it