https://www.techpowerup.com/reviews/NVIDIA/GeForce_GTX_1060/26.html
A GTX1060 is about 2x as good, however that assumes a high-end CPU.
The FX-8350 would bottleneck most games, though the amount varies a LOT. Some games might get 60% of the performance that a top-end CPU + GTX1060 would get compared to the FX-8350 + GTX1060.
*Fallout 4 is very demanding on the CPU (mostly because game engine core is OLD, but it's still a popular game so I'll mention it):
https://www.techspot.com/review/1089-fallout-4-benchmarks/page5.html
The performance is about 60% (with the same GPU, settings etc) compared to a good i7 CPU.
WORSE perhaps is that the FX-8350 can't maintain 60FPS in Fallout 4 which (on my PC at least) does not handle drops below 60FPS (60Hz monitor) very well. Some games with VSYNC ON handle drops okay, but for this and a few other games it is jarring.
DOOM would run very well though as the Vulkan API it uses allow the game to be well threaded so the CPU bottlenecking is reduced quite a bit.
https://www.techspot.com/review/1173-doom-benchmarks/page5.html
It's not there, so I'll just say about 115FPS for the situation described which is not only about 80% of what the best CPU can do, but more importantly is well above 60FPS so with the right settings you can for example, run a solid 60FPS VSYNC ON (60Hz monitor) if that's your goal.
Tomb Raider:
In the 2nd last TR game the FX-8350 does close to 100%:
https://www.techspot.com/review/645-tomb-raider-performance/page5.html
SUMMARY:
so how much bottleneck you have will vary, but again it should get between 60% and 100% of what the best CPU can do in terms of FPS average, with perhaps 25% or so being the average LOSS but that depends a lot on the types of games you play