http://www.techspot.com/review/1209-nvidia-geforce-gtx-1060/page10.html
The 1060 outperforms
on average the 480 (except in DOOM, where the 480 beats it), but the performance is pretty close (maybe an 11% edge).
That would be fine if the price was about the same range, except...
http://pcpartpicker.com/products/video-card/#c=373,370&sort=a8&page=1
If it's not even available, then it doesn't matter how much better it performs than the 480. Or, to put it another way, you can wait for the 1060 to become available, but you can purchase a 480 now & know that you're getting a card with almost the same performance
now.
EDIT: And, it seems that Tom's Hardware has decided that, for the money, the RX 480 is the better choice:
http://www.tomshardware.com/reviews/best-gpus,4380.html#p5
They recommend the 4GB model for "Best @ FHD (1080p) & Playable @ QHD (1440p)" (although they do mention that for those wanting more VRAM, they get the GTX 1060 instead of the 8GB RX 480).