Like the other poster the GTX 1060 card may perform a bit better, but there really is not much of a percentage in performance between a RX 480 card and the GTX 1060 card.
Games even a few titles right now are starting to use more than 4Gb of on board graphics card memory.
Mainly for higher resolution textures, take a look at the Fallout 4 Hi res texture pack LeviLAD.
It states 8Gb of video memory to be able to run the hi res texture pack just released.
If it`s any Indication then having a card with 8Gb of memory fitted to it vs just 6Gb on the GTX 1060 card it`s going to be the wisest choice to make if you want the card to last as long as it can when using it.
BTW ATI just released a new video driver anyway that give a 5% in overall game performance in a lot of new titled games made in 2016 and 2017.
So it`s very clear to me what the choice should be.