I would've said GO AMD a few weeks ago until my friends build bottle necked hard on his nvidia card. Weirdly hit and miss. Built about 5 pc's with FX 8350 with 1050 TI or similar cards and never had an issue with FPS at all, but my friend's 1060 bottle necked like crazy.
Pros of AMD: Cost efficient, good budget PC gaming builds, I'm running an old 660 ti on a CPU intensive game with an FX 8320 and I get 150~200 FPS (low).
Cons: Bottle-necking, not so good with nvidia cards for some reason (well some nvidia cards, check the thread about bottle necking).
Pros of Intel: reliable, faster, much less bottle necking issues. Needs less power, runs cooler.
Cons: Expensive.
I personally have had no issues with AMD processors and I can stream better than my friends with Intel processors for a third of the cost. But my friend just bottle-necked his CPU with the 1060 nvidia card so now I'm hesitant unfortunately. I think personally I'll stay with AMD because it's cheaper, and my 8320 has been reliable for years even when I'm not using the best graphics card. Sooo.. out of maybe 10 pc's I've build I've had one do badly due to a weird bottle neck with a 1060.
If you can afford it go for the Intel processor. If you want a budget build, check the bottle-neck guide before you purchase