Since you are talking about the 3GB 1060 vs the 4GB 480 I would have to go with the 480.
The reasoning is that I just don't think it makes sense to buy a card with less than 4GB of VRAM anymore unless you are in the low budget GTX 1050 range. Yes, the 3GB 1060 performs very similarly to the 6GB version in most games but there are some, like Rise of the Tomb Raider, that show a significant difference.
Since most popular GPUs from the last two generations (480, 1060 6GB, 1070, 1080, 4GB 960, 970, 980, 980 Ti, 390, 380, and even the older 290) have 4GB or more of VRAM I can see that becoming the new baseline for developers and more games...