I've never really used an actual GPU before (I am building my first PC with a dedicated one soon, all of my systems have used onboard graphics), but I'm ultimately going with Nvidia for a few key reasons.
Firstly, the AMD laptop I have just doesn't offer a great selection of graphics options. Now admittedly, a lot of that has to do with the fact that it is technically a lower tier graphics processor, but even then I've noticed that a lot of user guides on how to get older games running properly tend to lean towards Nvidia since most of the options don't seem available to even higher tiers of AMD cards. Now I'm pretty uneducated in this department, so I might be getting it totally wrong, but to me Nvidia seems like it would be easier to work with when it comes to messing around with graphics settings. Half the time the guides recommend you download some third-party software to get AMD to do what you want.
Secondly, AMD doesn't support OpenGL that well, at least not according to the research I've done and personal experience. A huge majority of my PC game catalogue consists of older titles, most of which run on OpenGL, and most of the time they run badly on my laptop, which is annoying because I had an older Intel laptop that ran those games just fine. To my extremely limited knowledge, Nvidia has better support for OpenGL drivers, and I like that.
Like I said, I'm not really experienced in this field, just thought I'd give my two cents on it.