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 becoming prolific (compared to Gsync), as many TV manufacturers have even stated that future releases will likely be compatible with this AMD GPU feature.