I would never take a cab in Rio de Janeiro or Sao Paulo, but I take an Uber frequently.
The really big difference for me here in Brazil, is that I can communicate to someone in case the route is bad, something is stolen, etc. Taking a cab is so ephemeral that I don't even have time to complain or ask for help.
In principle you could also do that with a cab company, right? So the difference is really that you trust Uber. If anything, it's not the idea that's great, it's either the brand or the quality of the service.
The really big difference for me here in Brazil, is that I can communicate to someone in case the route is bad, something is stolen, etc. Taking a cab is so ephemeral that I don't even have time to complain or ask for help.