As a former taxi cab driver, I can say it was inevitable that Uber/Lyfft or something similar was going to happen. Taxi companies are their own worst enemies.
Here's the real advantages/disadvantages between the two. (Using Cleveland where I'm from)
background checks only go so far. In Cleveland, background checks are done twice a year for taxi drivers. 3 moving violations within the year? You lose your hack license. So there is a certain assurance that the driver is capable.
Insurance. Regular car insurance doesn't cover an Uber driver. While he has a fare, Uber has insurance. But if the car is empty, the Uber insurance doesn't apply and the Allstates and State Farms won't cover commercial usage. All taxi companies are required to have insurance.
Taxi's are only allowed on the road for a maximum of five years and are inspected twice a year. Every dent must be fixed and every stain removed. All safety systems must be intact and in working order. Rules, although selectively enforced, are stringent about picking up and delivering riders.
That said, customer service isn't close. Dispatching is incompetent and downright corrupt.