Since you will be playing at 720p resolution you should get good FPS with the GTX 760 and Crysis 3 should be playable on the i3-3220. Especially since 720p is less than half the resolution of 1200p.
Between the Core i3-3220 and the FX-6300... In games that do not really care how fast the CPU is as long as it does not bottleneck the GPU (like BioShock) the performance should basically be the same. In CPU intensive games that only use 2 cores (like Skyrim), the i3-3220 will give you better performance even if the FX-6300 was overclocked. In CPU dependent games that uses 4 cores the FX-6300 will perform better than the i3-3220.
If you had the money, the answer would be to simply buy a quad core i5 CPU. However, since you are working with a relatively small budget the choice seems to be between the i3-3220 and the FX-6300. The vast majority of games only use 2 cores so on average you don't really need a quad core CPU. However, the specific games you want to play may be able to take advantage of 4 cores.
As stated, Crysis 3 is an exception, not the rule. Most CPU demanding games will be more like Hitman: Absolution (such as Metro 2033 / Last Light) were a dual core CPU will still good frame rates, but not as high as a quad core CPU can. However, if you look at the performance chart again you should note that while this game can make use of 4 cores, the dual core i3-3220 still outperforms the 6 core FX-6300, but only by 3 FPS.