Nvidia recently removed the driver check on consumer cards making them the clear choice now.

I've actually had good luck with AMD cards, but the reset bug is truly bizarre. For instance I own an evga R7 360, no reset bug, very reliable. I had also purchased an XFX R7 360, never survived a reboot! My sapphire RX 470 also works fine with no special actions from me and I've heard people have issues with that one.

You're definitely correct regarding anti-cheats though, they are something you have to watch out for.