We'll, the RX 470 and the GTX 1060 are slightly different level cards. The RX 480 and the GTX 1060 are on the same level. Currently, in most game benchmarks, the GTX 1060 has better performance then the RX 480. I would probably get the GTX 1060. Another thing to note maybe, is that AMD's FreeSync can be found on much cheaper monitors compared to Nvidia's G-Sync, so if you are maybe looking to replace your monitor soon with a nice FreeSync or G-Sync one, i would recommend the RX 480.
Another thing is, the RX 470 price has decreased by a good deal recently, the RX 470 for $135 whereas the GTX 1060 is for $230, the RX 470 definetly provides better price to performance compared to the GTX 1060. Also note that the RX 470 is about 7% slower...