In my opinion, AMD does have better results of the game isn't driver based (Certain games like Fallout 4 have more support for NVidia, so AMD will probably have less FPS and possible more problems)
well, there is no such thing as "driver based". you're thinking of Nvidia GameWorks, Nvidia's enhancement suite which includes stuff like HBAO+, TXAA, Hairworks, PhysX etc for easing integration into games.
no problem running all that on AMD except primarily for physx (which Nvidia outright refuses to make it work on AMD hardware) and Hairworks, which relies on tessellation and AMD cards are generally bad at tessellation. there may be a few other features (I think a few anti aliasing solutions) but those are the main two that really hit AMD hard.