It will be used in a gaming computer. I understand the 540 can be overclocked, but I was told the newer architecture of the 3220 makes it better/faster. Can someone verify this? Which would be a better choice for my GTX 560 (non-Ti)? Thanks.
the i3 3220 is much better
As Havok has said, the 3220 will perform much better.
That said, I generally don't recommend i3 chips anymore, if you can wait I'd suggest seeing what Intel newest line has to offer. If you can't wait but can invest a bit more money, going for an FX-6300 would be a more reasonable option. Even at stock the FX-6300 outperforms the i3 in many games and blows it away in any real processing situations, couple that with the fact the FX-6300 can be OC'd to nearly 5.0GHz on a reasonable cooler solution and you have a much more capable chip.
As programs and games become more complex, they will be utilizing multi-core technologies more and more, purchasing a dual core CPU at this time will severly limit the future usefullness of your purchase. While many games still more reliant on a limited number of cores, this trend is changing and you might as well be ahead of the curve.