With the latest drivers, the GTX 1060 (6GB) and RX 480 (8GB) are basically neck-and-neck now. Earlier comparisons are no longer valid between the two.
https://www.youtube.com/watch?v=gEw3CaNSbUo (Hardware Canucks)
This was a comparison from mid December 2016 for both cards.
While it's not a surprise that Vulkan or DX12 performance was seen to be better with the RX 480, the most significant observation was that in DX11 the two are very close now. Drivers have possibly improved since those tests too.
The RX 480 might have an advantage due to extra vram, although the GTX 1060 may OC better. Having said that, the likes of the recent XFX RX 480 will OC much better than earlier reference cards and even some custom cards.