The latter is almost instantaneous. On a really cold night a few weeks ago I couldn't get my car started, nor could AAA. How to go pick up my takeout food? He suggest Uber (taxi company had a wait of 10 people ahead of me.)
A minute to install, a few more to enter my name, address, and CC info, then enter destination and push a button. Wtf, ETA of Uber driver 6 minutes???
Standard taxies and the politicians who protect them can go drive off a cliff.