Synthetic benchmarks put the 580 about 15% ahead or behind the 1060 depending on which test they ran. The on-board memory is 8GB vs 6GB which might help if you're running high resolutions. Price seems to be pretty similar. Were I on a strict budget and running 1440p or 2160p, I'd probably favor the 580. If I had a couple hundred extra, I'd just get a 1070 and be done with it.