It really depends on where you are. My favorite comparison (because I experienced both) is Germany vs South Africa.
In Germany, the cabs belong to the company and drivers are employees (not going in debt for medallions like in the US). The cars are usually in good shape Mercedes and the system is 2-tiered: Taxis and Funkmietwagen (callable cabs). Taxis are allowed to use taxi only roads, can wait for walk-by passengers, are more expensive and pay higher licensing fees. Both can't just tell you "No" without very good reason.
Funkmietwagen have to follow normal car rules, can only be called in advance, usually have slightly cheaper cars, but are cheaper.
Uber tried disregarding the laws in Germany, was told "No" and now is only active in some very few cities and only with their higher end service, operating as normal Funkmietwagen.
The only thing they accomplished was improving the app situation.
In South Africa, it's very different. Taxis cost 3-5 times what you pay for an Uber, are often old, shoddy cars and certainly like to decide not to pick someone up (which I think is technically illegal).
Uber is thriving and mostly seems like a safer and better solution there.