AFAIK, Uber works in NYC the same way as it works anywhere else in the U.S. (At least as far as passengers are concerned.)
Yes and no. The advantage in NYC is that you get a licensed driver who has been checked out by the TLC, and has appropriate insurance. In other areas (such as San Fransisco, where there was a death that insurance refused to cover since the Uber driver is considered to be a taxi driver), you may run into problems.
In short, Uber in NYC will have a more professional and better insured driver than elsewhere, so that has to be considered in the response.