Well, 1060 wins most DX11 benchmarks. DX12/Vulkan is pretty much 50/50.
1060 wins in RotTR and AotS.
480 wins in Hitman and Doom.
1060 tends to overclock better:
Problem with RX 480 is most custom cards are too noisy and they are out of stock everywhere, and priced higher than MSRP.
Custom 1060's can be found in stock for 250$.
MSI RX 480 Gaming is the first custom card with decent noiselevels during load (31dB). Nitro and Strix are almost 40dB load.
MSI GTX 1060 Gaming is 28dB.
Decent cards for sub 1200p gaming - 1440p not so much, but some will find it acceptable, I guess.
As you can see, custom 480 still loses to reference 1060 overall. 1060 rivals Fury.