it depends, they are both good and about equal in performance, they both have they're strengths and weaknesses. I've had them both and they are extremely good cards and great values.
gtx 1060- uses a lot less power and typically will be a cooler running card.
rx 580- has freesync, performance in FPS will be ever so slightly higher in a lot of titles but uses gobs of power and can run a little toasty.