The 1060 3gb is not faster than the 480 4gb, in DX11 they are equal in performance(averaged over multiple games) and the 480 pulls ahead in DX12 and Vulcan. Yes, DX12 and Vulcan performance makes a difference as it's adoption is happening much faster then DX11 did. More and more games are adding DX12 support and this will only increase going forward.
The 1060 3gb is NOT a 1060 6gb with less VRAM, nVidia disabled part of the chip. While the 480, as mentioned by the other poster, is the full chip but with half the VRAM that runs a little slower.