The difference betwee a cab and a car service is that car services are flat rate while cabs let the meter run. If you end up in a traffic jam due to an accident or volume the meter is running even if you aren't moving.
Also many car services will make a stop for groceries or alcohol or whereever (I had one stop at my credit union once) for up to half an hour at no additional charge--cabs will let the meter run.
You should let the car service know in advance that you want to make a stop, and it's customary to add a bit more to the tip.
I've been in plenty of cabs and car service cars, and overwhelmingly the car service vehicles are cleaner and more comfortable than the cabs.
Depending on who you choose, a car service will often run the same amount r/t as a cab, with additional benefits. And like I said, if you get caught in traffic a cab could end up costing a LOT more.
Anne