The FX-8350 technically has about 33% more raw execution capability when all 8 cores are saturated than the i5-4440, meanwhile a core of the i5-4440 is about 35% faster than a PileDriver core.
If you were picking a CPU for a productivity application that could scale into 8 cores as easily as it could scale into 4, then the FX-8350 would be a solid contender in it's price class. Unfortunately, real-time workloads like gaming scale proportionally into core performance, not into core count (performance scaling into core count tapers downward with more and more cores, some game engines and GPU driver/API implementations scale better than others into many-cores). Overall, in most games, the i5-4440 is actually the stronger CPU.
If you...