Freesync is good. I wouldn't hesitate to use an RX580 and enjoy it so it matches your monitor. Ensure your CPU doesn't bottleneck the video card so you get maximum use form the video card.
The 2060 is out end of October - from leaked documents, but depends how desperate you are.
I prefer the AMD because Freesync monitors are so much cheaper than Nvidia (+150 for the same monitor with gsync).
The 580 - beats the 1060, but won't beat the new 2060, that i am sure of.
Freesync is good. I wouldn't hesitate to use an RX580 and enjoy it so it matches your monitor. Ensure your CPU doesn't bottleneck the video card so you get maximum use form the video card.
From what i saw in benchmark leaks gtx 2060 has almost same performance as gtx 1080. i might regret buying rx 580 early if gtx 2060 launched at same price but in much better performance.