580 is a generally better card however it depends a lot on the specific model, as the chip is pretty hot and power hungry. 1060 6G is pretty close behind in performance but is going to be fine regardless of model. If it's a 1060 3gig you shouldnt even consider it.
Not true. Both are very very close in terms of performance except the 1060 comes ahead in most games. Ofc the difference is generally abysmal so i wouldnt look at it this way and instead would consider the slightly smaller price on rx580 and that extra 2gb vram is what makes it overall a slightly better choice.
And theres also crossfire thing, 2x 580 will probably be as good as 2070 super if not even slightly better. Thats main reason to go for 580 these days imo.
RX 580 is just a better card in general, except you're doing video editing and playing alot of ubisoft games (because ubisoft games is much better optimized for nvidia) then 1060 is better suited for you
I would say raw performance per dollar-wise I might go for the RX580, but as a user, I think Nvidia's has better software and power efficiency wise also it has Cuda cores so if you are video editing that's a great advantage (the 3g model doesn't have Cuda cores