You need to think about your requirements, now and in the future. For 1080p gaming right now, I'd say the 1060 3gb is the best buy at $199. The 1gb extra that the RX 480 4gb gives you is not going to do anything for you right now.
If you believe Directx 12 and/or Vulcan will be important in gaming in the near future, the 480 would be the better bet. If it takes too long for DX12 and Vulcan to take off, then it's probable that neither the 1060 or 480 will be good gaming cards at that point.