A US perspective
....or at least a US East Coast one. I don't often have the occasion to to take cabs, but when I do, I find that they often don't arrive when booked by phone (or if they do, 20 to 30 minutes later than the booked time); that they are rarely available for being flagged in large cities when the weather is poor (good old supply and demand, right?); and they are often driven by people who speak English poorly, if at all, even if they do know their way around a GPS device. The vehicles, at least in New York City, also appear to "feature" obnoxious, large video screens a few inches from the customer's face advertising I don't know what all, at high volume. (That's where being able to communicate with the driver that you;d like the damn thing turned off entirely is a help.)
Contrast this with my experience to date with Uber, in NYC and Boston: the car, whether a black car or UberX (ordinary vehicle, usually a hybrid) arrives on time, I know where the car is from the moment of booking, the driver knows in advance what his/her tip will be (tipping being a very big deal in the US), and so far, 2 for 2 on being able to communicate verbally with the driver – not that Uber rides have obnoxious video ads in them, either. (I'm guessing the last is due to recent immigrants' being less able to navigate the odd requirements from establishing themselves as independent operators, vs. receiving help from other members of the same community who have established taxi businesses.) And finally, the unholy taxi monopolies (a small number of companies, who sit on municipal taxi regulation boards as well as providing the "service") resist requiring the acceptance of credit cards for taxi service.
Given all of the above, in this area of this country at least, yes, Uber delivers a distinctly superior product for only a small premium in price. That said, the competition between them and Lyft appears, in some markets, to be of the Wild West variety.