580 is better. It'll handle 1440p a whole lot better than a 1060 will. Think of a 580 as somewhere in between a 1060 and a 1070. Both are capable of 1080p without issue, so max fps is meaningless, what you'll be looking for is minimums above monitor refresh. As said, some game engines prefer nvidia, some are happy with Amd, so in the specific games you are concerned about, as long as either card gets decent minimum fps, the winner will be the cheaper card. This can be affected by your psu though.