The flat fare is only from JFK to Manhattan(source: http://www.nyc.gov/html/tlc/html/passenger/taxicab_rate.shtm...), not to JFK, or to/from LGA, and not to the other boroughs. UberX also comes to my apartment, while a taxi rarely does, and the drivers are typically more patient with me strapping my son's car seat in (or providing one in the case of Uber Family) and even helpful.
As someone who does not live in Manhattan, I can say that I'm far more likely to be able to get an Uber than a taxi outside of Manhattan (although it's a little better now with the Green cabs). And, I've never had an Uber driver keep their doors locked and speed away at rush hour when I told them I was going to Brooklyn. My utilization of taxis in NYC is entirely different than my utilization of UberX.
I'm sorry that I missed that phrase. I don't have experience going to/from the one of three NY area airports that has flat taxi fares because I live in Brooklyn, not Manhattan (and Brooklyn applies to the analysis of Uber in NYC). There is definitely no need to be unkind to me about it; I'm sure you've misread something at least once.
As someone who does not live in Manhattan, I can say that I'm far more likely to be able to get an Uber than a taxi outside of Manhattan (although it's a little better now with the Green cabs). And, I've never had an Uber driver keep their doors locked and speed away at rush hour when I told them I was going to Brooklyn. My utilization of taxis in NYC is entirely different than my utilization of UberX.