This is actually a very good question, thanks for asking it. I could come at this in multiple ways, but I don't think there is much argument that there is something "missing" from not switching over to NVIDIA from AMD. NVIDIA doesn't really offer much different, unless you're talking about doing something more exotic, such as a multi-monitor setup.
NVIDIA do have PhysX, but PhysX supported games are few and far between. Even when they do have support built in, it's not like the entire game world changes that much to the point of "I must own an NVIDIA GPU, right now!"
I personally think NVIDIA's multi-monitor tech is better, I've had a much simpler time setting that up and running it than I ever did with my Radeon GPU setups, but this changes setup to setup. It would really depend on the setup you've got, and which GPU. You would probably benefit upgrading to an NVIDIA card, as they offer some great price/performance ratios right now.