I got a 6gb 1060, because I think I just like Nvidia's driver support so much more. It feels like they are much quicker with updates, and the RX480 is just a dab slower and I was able to get a 1060 for less than 50 dollars more than a 4gb RX480. Plus, with my heating/cooling setup, a blower style card makes more sense, and I was able to find an ASUS one I liked for the 1060.
That is really it, they are basically the same, RX480 is a bit cheaper, and a bit less powerful, and that is about it. I am sure they are good cards. It really comes down to vendor preference, and availability. I kind of had a hard time finding an RX480 that I wanted from XFX or Sapphire that was the 4gb version. They seemed to be pushing the 8GB card hard, and the extra VRAM isn't worth the 50 dollar jump in price.
There are some killer deals to be had, however.
RX 480 4GB (MSI) 225$ (Great deal)
The 1060 I got ASUS Turbo 6GB 260$ (Also not bad)