The prices are somewhat equitable for the 6Gb 1060 and 8Gb 480,so that's really of no concern other than to point out differences in brands and editions. In the games where the 480 wins out, it's by @ 5fps on average, where the 1060 wins its by @8fps on average, so no real difference in performance for the most part. There are games that show large nvidia optimization, there are games that feed amd cards much better, so taken as a whole, there's no difference in cards.
The biggest differences are not in performance or price, but in the gimmicks. The 1060 uses less power and generally runs cooler. The 1060 has native physX support, amd doesn't, so uses more cpu power to compensate. The 1060 is a stand alone card, cannot accept sli, the 480 can be crossfired, a decent budget option for more power. Some swear by amd, some prefer nvidia. With these 2 cards its really a personal choice, or a choice to fit needs or looks. Either will work equally well at 1080p