My take on this is that the performance difference between both is insignificant even in DX12, go with whatever other features you like, for example the 1060 runs much cooler and quieter, for me that is a huge deciding factor when buying a GPU even before performance, Nvidia software is superior, things like Shadowplay, game streaming, Geforce experience and game optimization.
For the next year or two where most games will still come in DX11 the 1060 will be superior and by the time DX12 becomes the standard much better cards will be in the market and either the 480 or 1060 will be obsolete by then.
If you can get the RX480 significantly cheaper than the 1060 then go for it, otherwise if prices are the same i would go with the 1060...