The i5 has better per-core performance while the strength of the FX lies in its core count. Most games don't really use that many threads and cores that the AMD has to offer as of now, so it is the weaker choice in my eyes. But the AMD will get on the i5's level as time goes on and new games add compatibility to execute their code on all cores. It's a matter of future vs now. But if you do choose the AMD, keep in mind that it will be relatively weaker in the future vs processors of the future. The i5 will show its age in the future as well, but it will have enjoyed its glory days when it was out on top.
Get the i5 for performance, FX for price. If you choose the i5 route though, I recommend the 4460 (~$190). Costs the same as the 4440, but is slightly faster by 0.1 GHz and runs on the new Z97 boards (with backwards compatibility to the Z87). The 4440 can only run on Z87, so you can't upgrade to Broadwell if you choose to in the future.
The i5-4590 is has the best price-to-performance ratio of the i5's, but costs $10 more.