Well you know it really comes down to budget and your exact needs. Intel is king of single core performance at this point in time. So any application that runs on one core or thread is going to run much better on an Intel system. Applications that utilize a lot of multithreading the processors are going to be near even, even closer if you go for the FX 8370. In Cinebench the FX 8350 @ 4.5Ghz and the i5 6600K @ 4.5Ghz are nearly even. Not bad considering the age of the FX 8350. Now in most games the edge is going to go to the much newer arch of the i5 6600K and the fact that all games we can benchmark right now are on DX 11 which heavily favors single core performance. How the two will do with DX 12 games is yet to be determined, however the gains for the AMD 8 core processors could be big.
Biggest pro for i5 6600K is the huge single core performance edge it holds and a much newer arch, much better power management.
Biggest pro for FX 8350 is very good multithreaded performance very good multitasking. FX 8350s have been proven to overclock to 5Ghz, I doubt the 6600K is going to hit 5Ghz. The FX 8350 is going to be cheaper than the i5 6600K. Now if you are serious about going with the FX 8350 I would recommend going with the refreshed FX 8370. The FX 8370 has AMDs very best binning, power management and performance tweaks. It is slightly ahead of the FX 8350 clock per clock but overclocks with less Vcore (less heat and power) and can on average hit better overclocks. My FX 8370 is running at 5.5Ghz @ 1.55V totally stable, best I ever got out of an FX 8350 was 5.1Ghz @ 1.55V. Now you have to have a good motherboard, and cooling to tame an overclock like this, but she benchmarks well above the i5 6600K in multithreaded applications as to the best of my knowledge no one has ever gotten an i5 6600K to 5.5Ghz, and clock per clock they are just about even in heavily multithreaded benchmarks / applications. Now as stated single core Intel rules the roost.
So it really comes down to your exact needs, and your budget. The money saved on the FX 8350 / FX 8370 can be applied to getting better GPU for example, however if you run a lot of single threaded applications then Intel is really the way to go. As far as power usage goes, yes the FX uses more power, produces more heat (you'll need a good cooler), however its not going to jack your electric bill badly, at most left to run non stop 24/7 your talking a couple extra bucks a month.
Now if your budget can swing an i7 Skylake, forget about it, Intel all the way. The FX 8370 can hold its own against i5s in heavily multithreaded applications but gets totally dominated in every way by i7 Skylake.