With the sheer price difference with overinflation, the GTX 1060 3GB is going to be your best option. It's only been shorted slightly and will only have trouble running higher resolutions and large, complex textures with the low amount of video memory it has.
But that also depends on what games you're playing and what you're anticipating. If you're planning to be playing a lot of games that are coming out that have either Vulkan or DX 12, get the RX 480.
However, if you're planning to stick to modern games that are already out and not coming out, then the GTX 1060 is going to be the better of the two.
AMD always gets ahead of themselves. The RX 480 is more futureproof than the GTX 1060, but you've got to consider which titles you're going to be playing instead of graphics power with the two of the card's performances running near the same.
With some aftermarket RX 480s, they can match the speeds of the GTX 1060 6GB in all games but heavily Nvidia based titles. But that also requires overclocking a graphics card (which just takes time and isn't actually that hard) and getting the correct AIB partner card.