I think I heard NVIDIA cards are better for zcash mining and generally more power efficient but other than that the AMD counterparts are better for mining because most miners are implemented in opencl not in cuda.
And the Linux support is probably better on the AMD side.
I have both the sapphire nitro+ rx 580 and the Asus gtx 1070 8gb, they are both great cards for mining, but let me break out the differences i noticed so far:
-They both mine ether well but the rx580 does much better job on DUAL mining ethereum+dcr/sia : I have 30.5Mh/s eth + 850Mh/s decred on 580 while 30.5Mh/s eth + 205Mh/s on 1070.
-The gtx1070 uses less power, and mines zcash better.
-You have to bios mod the rx 580 to get a decent hash.
-You cannot bios mod the 1070 (you can't bios mod nvidia cards), but just using the MSI afterburner is enough to overclock/undervolt you nvidia cards.
-The rx580 was cheaper for me.
so as you can see, it's not really big differences between these two, so which ever you find you buy and start mining !