I'm not sure about NYC, but it is cheaper in London to get an Uber than a taxi.
I've heard that the bonus of London black cabs is that they have super knowledge of London.
I've found this to not be the case. Sure, it's good. But in all honesty I find google maps to be better.
Let's also not forget that Uber started as Ubercab and was forced to change their name. I don't think they ever intended to be a limo service, and their current product offerings are largely not limo services.