Look, I don't want to start a rivalry here, but in my opinion the FX chip wins. It is cheaper than the i3-3220 which isn't a direct competitor but has similar performance. The FX CPU is faster in multiple thread applications, can be overclocked much easier and is backwards compatible with both the AM3 and AM3+ boards. With the core i3, you need to do an enormous bios update on sandy bridge 1155 boards to make it work which is risky (some of the time) and you cannot overclock it, which makes it a bummer for gaming enthusiasts who want a budget gaming system.
Sure, the i3 wins in some things but so does the FX CPU, in some things. The FX CPU wins over the i3 overall in value for money, compatibility and, in many things, performance.