They are both very comparable performance-wise, so really don't think it's worth regretting or switching. I still tend to like the AMD offering at this price point though, as the 480 can be paired (Crossfired) in the future if higher resolutions or frame-rate were wanted more affordably than a whole GPU upgrade, whereas the 1060's cannot:
http://www.amd.com/en-us/innovations/software-technolog...
But more importantly they work with FreeSync monitors:
http://www.amd.com/en-us/innovations/software-technolog...
Which is a very affordable way to get adaptive sync in a next monitor upgrade (which are less expensive than the Nvidia counterpart, Gsync):
http://www.geforce.com/hardware/technology/g-sync
That and FreeSync is on the road to...