In the last city I lived pretty much all cab drivers were also Uber (black) drivers (or maybe it was the other way around). Regardless, pricing was very similar and often cheaper going with the regulated taxi rate.
Sometimes. I like not handling credit cards and cash. They're faster and more available in areas where taxi services are not great.
On the other hand, I had an Uber-X driver just today drive right past a clearly marked airport terminal entrance because his GPS didn't direct him there and "he hadn't been out to the airport in a while." It's unlikely that would happen with a cab.
I particularly remember taking a cab in Las Vegas many years ago trying to get from one end of the strip to the other. I was an obvious tourist - so he took the "faster router" around the city - just to "realise" that the exit he was going to take was blocked due to construction work and he now had to do a huge detour.