It's always been that taxis don't come when I need them. Sometimes they're fine if you're at a bar and a cab will come by for hailing because they know business will be there, but if you're carless and need to get somewhere at a particular time cabs have always been a nightmare.
I've called to get a cab to come pick me up and then waited 2 hours while dispatch couldn't find a cab to come because they were all too busy picking up opportunistic rides. I've never had an experience anything like that with uber or lyft.
I would -- and now that the money train has dried up for uber a bit, do -- pay as much for an uber as I did before for a cab, except now the uber actually comes. In my particular city most cab drivers also aren't union, and they pay to rent their cars for their shifts from the people who own the plates. Most of the protest of uber coming to town was from cab owners (some operators, but many not) who were using their license as a retirement plan.
I recognize that the drivers were put in a tough spot, and most of this isn't their fault, but things were deeply broken before, and they still are. But I think there's a lot of rose tinted glasses going on here, and people who needed cabs were often literally left out in the cold by the way things were.
(1) Pretty much the only city I've ever had good experiences with cabs is NYC.