I just installed my 580 yesterday, so I can provide a couple thoughts.
A 1060 might be better, in particular in regards to power consumption, but I'm still happy with it (it replaced a 970). I do run 4K occasionally, and the extra VRAM blows away the 970, it can just do more on screen stuff - Windows was showing that in Fallout 4, on ultra settings it was using close to 5.8 GB VRAM. The 970 would either bog down, or the game would crash. Drivers I like quite a bit too, I originally bought the Nvidia, as the old AMD drivers weren't great, but then Nvidia's were that great either. The new AMD ones are pretty nice.
I also run a 3 monitor setup, and AMD handles it miles better than Nvidia. I don't have any DX 12 games, so I don't know/care at the moment.
I also got the 580 for $250 2 weeks ago through Best Buy, which is probably were it should be at this state of the art, but with how ridiculous GPU prices still are...2 year MSRP shouldn't be celebrated online, but here we are.