Taxis in my area (Seattle) drive fast and loose, at least they did 4 to 5 years ago. No signals, always about 10MPH over the limit. Music always on, not loud, but usually always on.
Lyft/Uber drivers in the area were/are a little more gentle (the ones that weren't taxi drivers before). Interestingly, sometimes I'll get a Lyft driver that asks if I care about how fast I need to get to my destination and how I'd like them to drive.
Also, I took taxis in Prague during vacation, and that system is amazing and I'd choose those taxi services over Uber/Lyft any day. Clean, quick, stupid simple, and the drivers were pros.
The majority of taxi drivers I come across are terrible drivers. They pump the brakes on the highway when there is no traffic, they go slow in the left lane, make illegal turns, and don't know where they are going.
Lyft drivers are hit and miss, but for the most part, are people who are good at driving and getting where they are going. Plus they all use waze or Google Maps, so their directions are good.
I've had to exhort a couple of Lyft drivers (I try to avoid the other one) to go faster to keep up with traffic, but other then that, they are on average 2 steps above taxi drivers in terms of alacrity and situational awareness.
(This is in the Washington DC area BTW)
I don't have the same careless experience when I take a taxi. Of course, this is anecdata only, but the fact that there are virtually no requirements make me worried. I only take Uber/Lyft if someone else is ordering it (when we're in a group), otherwise I'll find other options with actual professional drivers or public transportation.