In Houston there are no cabs roaming the streets to hail. You can call and schedule ahead of time, or do it online like I do. They have been reliable. Never used a car service but we have those too.
Brooklyn hasn’t been a city since 1898
As well, the ‘black car service’ industry began in NYC in the late 1980’s because up until then you could call ahead for a yellow cab. The medallion light on the top of the car had a separate ‘On Radio Call’ panel that would be lit so that people on the street would know why their hails were being ignored.
It was the abuse of this system (drivers not wanting to pick up fares in certain areas, not wanting to pick up minorities, not wanting to pick up fares in the rain, etc.), that led the TLC to create a new category of licenses.
Besides that it was also an incorrect statement, that is what I was going to say.
Otherwise, the question has been answered. In NYC, you cannot call a yellow cab, and you cannot hail car service. As for car service, it runs the gamut from raggedy cars that would probably fail inspection to upscale services. Generally speaking, you get what you pay for. While there are yellow cabs in the outer boroughs (well, maybe not Staten Island, but I only use SI to pass to southern Jersey), there are fewer and you won’t find one to hail except in certain areas (unless you are really, really lucky and find one just after a drop-off).