Nothing as complex as GPUs are ever going to be a simple comparison, but on balance I'd call this in favour of the 480. I think 4GB is going to be sufficient for a long time, so I don't give either the 1060 points for having 6GB or the higher 480 for having 8GB. 6GB and 8GB are both just marginal extras over 4GB for quite a while, imo. At least at this level of processing power.
So assessing it on performance, they look pretty darn close to me with the 1060 being ahead generally but only by a bit and losing out in some significant cases. In particular, the 480 seems to be better with DX12 games in general meaning that it's going to improve against the 1060 over the next couple of years. Secondly it is cheaper. Thirdly, and this is quite a big deal I think, the 1060 can't do mGPU. The 480 can. That means everyone buying a 480 has a moderately cheap upgrade path whilst people with a 1060 are stuck trying to sell theirs to buy a more expensive card. Given a general expectation that mGPU is going to be a LOT better supported in the future than Crossfire or SLi ever were, I'd strongly favour the 480 for that reason alone. Given performance is roughly similar and the 480 is cheaper, that's a decider for me.
EDIT: I should reference power consumption in the 1060's favour, though I don't care about that much myself.