The biggest difference between them are their different technologies.
Nvidia has Adaptive-Vsync, PhysX, Shadowplay, SLI and others.
AMD has Mantle, True Audio, CrossFire, TressFX and others.
It all really depends on which company has the most compelling technologies.
I'd have to disagree - with the new MSRPs, AMD blows away Nvidia on price/performance. And on performance with the R9 290x. But when you take into account the miner fools driving up AMD prices, if you're in the market for a card right now, Nvidia may be your only realistic option. Otherwise wait for prices to go back to normal. Oh and with RadeonPro, AMD cards can do Dynamic Vsync which is what I suspect is the same as Adaptive Vsync.
Also while Nvidia focused their efforts on 3d display, which hasn't really taken off in the market, AMD has been focusing on multi-monitor. If you want a seamless, 1 minute setup desktop/gaming system sprawling across 3-6 monitors, AMD is the only way to go.
Personally I have gone Nvidia but my reasons are not strong enough to tell someone else to do the same. There are millions of happy gamers using both Nvidia & AMD. If there is a technology you like for a game you want play that may swing your decision.