You can clearly see the 3GB outperforms the 480 in warhammer in DX11, in addition to every game that prefers Nvidia cards, and there are a lot (GTA V, Tomb Raider, Assassins Creed, Blizzard games, etc.). The 580 is slightly better than the 480. Again in any game that prefers Nvidia, even the 3GB 1060 is going to win.
It's also cheaper.
Not every game supports DX12 so arguing that it's better in Dx12, which is 100% true, is pointless. However there are MANY games in which the 1060 3GB can and WILL outperform a 480. The 580 may edge ahead slightly but not enough to definitively say its better. If anything they are evenly matched, which they are because the AMD WILL NOT win in EVERY case, so saying it's better is blatantly denying the cases in which it is WORSE.
With the 3Gb being cheaper it is clearly the better option.