The 1060 6GB and 480 8GB are quite the debate, I guess this is the battle of the lower versions of both cards.
With a Freesync capable monitor, an AMD card makes the most sense.
Between the 1060 & 480 the 'wins' appear to swing back and forth. The RX480 has a bit of an edge with DX12 titles currently, but I would expect nVidia to close that gap with a driver update.
With a Freesync monitor, I'd be inclined to recommend the RX480 to you - although neither card is a bad choice, the 1060 3GB should never have been called a 1060.