RX480 is a good alternative to the 1060, it's ahead in some categories/games, and behind in others, it's very close to call IMO, and comes down to what you want. One area where the 1060 has a noticeable, albeit not huge lead, is with VR units and with heat/thermal. Again, it's not huge, but it is somewhat significant from most the of the reviews/tests out there. Not that VR is really something a 1060/480 is optimal for anyway, so it's almost a moot point to me.
Some of the upcoming, and even existing AMD CPU/MB combos make a good case for building a 480 system so far as a mid range budget build. Also, availability, 1060s up here are hard to find at times, while the 480s seem to be in stock pretty consistently. I might build an AMD system once the black Friday deals start, haven't had one in YEARS, the 5770 card was the last AMD anything I've run.