I don't know how well cab drivers ate vetted — at least where I live. I don't take taxis often, but I've had some bad experiences. One guy tried to take me the long way home from the airport — to get more money out of me. Another one tried to pick me up and not in a cab. One blared loud music and refused to turn it down when I asked him to. And I could go on.
Uber drivers may not be as safe, but I wouldn't necessarily say all cabbies are better.