Snif, snif.... Ohhhhh! I can smell the nvidia fanboy here!!!!
6 month ago, before the release of the 580, pretty much everyone with common sense and unbiased opinion was saying that the 1060 6gb and 480 8gb was neck to neck and the winner was mainly depending on the game that youre playing on (some game perform better with the 480, and others with the 1060)... So now that the 580 is out and perform better than the 480, you're still saying without any doubt that 1060>580??? Cmon!!!! At least you could say that each has their strenghts.... The truth is, and look at any benchmark, game still using DX11 has a tendency to perform better with the 1060 and other games that use the newer engines DX12/vulkan perform better with the 480/580...
So AnasNazim, dont listen to Jowen... The best advice that i can tell you is, look at what game youre gonna play, do some research on internet about those game and how they perform with 1060 compare to the 580 and choose from there the one that suits you best. One other thing that you may want to take in consideration, is the fact that more and more game will be release in a future not that far with the newer engines DX12/vulkan and consequently, less using DX11. So, if you want a card that would probably be more futureproof, AMD is probably a better choice. Finally, dont forget to compare the price of the card, since that the price could vary a lot depending of the country you live in. Does 5-10 fps (on either side (1060 or 580) really worth the price difference... (if its 5$, probably not, 100$ is another question)... Only you can decide if the price difference worth it.... But, at the end, whatever will be your final choice, either card will give you great performance for 1080p, 60hz gaming at ultra setting!!!
Have fun!!!