The 8350 isn't bleeding edge by any means, but it does pretty well in games and should be on par with a mid-range Core i5 if not a bit better. If you have it overclocked a little then you're going to that much better off.
Given your choices are between a GTX 1070 + FX-8350 or between, say, a Core i5-6600K and a GT545 I think it's pretty obvious the GTX 1070 is going to be your better choice.
Note that the GTX 1070 *may* be a *little* bottlenecked. It doesn't mean the GT545 with a Core i5 is a better choice! What it really means is that you may not get any performance benefit from the 1070 over a slower GPU, like a 1060. I would be slightly surprised if the FX 8350 can't handle a 1070.
Still, work with your budget and see if a...