Payment options/scams = Uber lets you pay however you want through the app/apple pay without any need for cash, with an upfront price. Most taxis only accept cash, have unclear pricing that you only know at the end, can easily pad the meter in various ways, and may extort you if you really need a ride.
Refusing pickups = Uber drivers don't know the destination until you get in the car, and get kicked off the network if they cancel too many rides or abuse riders. Taxis are notorious for ignoring people based on looks, destination, convenience and usually won't deal with any trip they deem is not worth their time.
The difference in service and safety is magnitudes better with ridesharing vs taxis, that's why they're so popular.
"Sorry, the meter is broken"
"Sorry, the card reader is broken, cash only"
"No, don't worry, this is really the fastest way"
Also your Uber driver doesn't know your race when he accepts your ride or not. Which is probably why I find it a lot easier to get an Uber than a taxi.
Not being able to hail a cab due to racist drivers is a problem. However, in your example, the Uber driven can see your name, which is a pretty reliable proxy for your race, unless it's highly generic like John Smith or something.
Taxi drivers have to accept cash and cannot force you to pre-pay for your ride like Uber can. That at least reduces the number of drivers who would otherwise refuse to pick you up because of a perception that you wouldn't pay.
There’s plenty of reasons to have some regulation. What was missing previously wasn’t regulation, it was competition.