The 1060 is currently running better dx11 games, but in the future, more games will be developed with dx12, and the rx 480 runs those games better, but of course you can always play dx12 games in dx11
If you really want my opinion... I would go for which ever you can find a better deal on. They are pretty close and will both give you about the same experience
They both will last about the same. The 1060 is showing better performance now, but the 480 is showing better DX12 performance (at the moment).
What are the prices you are looking at?
The 1060 is currently running better dx11 games, but in the future, more games will be developed with dx12, and the rx 480 runs those games better, but of course you can always play dx12 games in dx11
By the time games are using DX12, it will be time to change the graphic card, both 480s and 1060s will be underpowered...
1060 is the right card right now, and for the next 1-2 years coming.
I would say the 1060 6GB variant is the better choice overall, would note that games that utilise Vulkan can have massive improvements on the RX480 but they aren't in huge numbers yet. In terms of raw performance the 1060 wins but with the help of DX12 and Vulkan the RX480 pulls ahead. Look at the games you will and want to play and make your decision from there.
@LeKeiser - 1-2 years maybe (& that is still title dependant anyway) it's swings & roundabouts between both cards now on different titles.
3-4 years as the op has stated ??
My money would be on the 480 in that respect.
Looking at things historically and cards have always aged better right from 3-4 generations back.
R9 280/HD 7950 vs gtx 760
280x/HD 7950 vs 770
390 vs gtx 970
On currently titles which aren't entirely nvidia biased all those amd cards now perform better than their comparable nvidia counterparts.
Nvidia have a huge edge on power & efficiency , that's all IMO.both cards are viable choices, neither will disappoint .
When looking at the market id compare likewise models personally , you'll pay $30 or so extra generally for a comparable nvidia card to an amd one.
Something to think about though, the overclocked 480s, like the Nitro+, are 480s pushed at their limit, and they are still a little behind non overclocked 1060s... Not by much, not everywhere, but still.