I think it might be a mistake of dividing the options into two camps, Uber and all other taxi companies, by now.. There are a LOT of IT solutions any taxi company can rent that gets them a lot (or most?) of the Uber features (except the brand name). Basically all of the IT you need including apps and call-center handling can be sourced in.

I guess tech is catching up with Uber and what they still have is a good brand and there is some confidence that you hopefully has a smaller risk of getting ripped off with them at least if you're a tourist in a new city.