If you need a card now and don't plan to change it for the next year.... Go for the 580..... Its pretty much sure that Nvidia will drop new cards this year..
AMD kinda cater their drivers better with time.. Not a fanboy by any extend... If I had the money I would go with a GTX 108ti and an X34 or a pg348q with gsync any day.....I bought an R9 Fury and a freesync monitor early last year.... Kinda got into the "wait for Vega" hype only to got stuck with it.... To make the story short, got pleasantly surprised playing doom on Vulkan and other games that use DX12 ... Fps went up significantly... In my experience don't jump into amds fresh drivers right away....
Like others mentioned, 980ti would be best bang for buck if you can get a good price. Otherwise, if it's between RX580 and GTX 1060, I would go Nvidia. AMD processors are fine, but their GPUs are garbage IMO. At least if you're not crypto mining...