Rather than post game benchmarks which anyone can find out, here are the major differences between the two processors. A quick Google search can confirm all this.
1. The i5 has a much lower TDP, meaning less energy usage and less heat and noise.
2. The i5 has very strong single-threaded performance.
3. The i5 uses the LGA1155 socket, which has been replaced with LGA1150.
4. The FX is unlocked and can be overclocked.
5. The FX has good multi-threaded performance, but comparitively weak single-thread performance.
At face value I'd recommend the i5, but that depends on your budget.