I've been in NYC for a week, and I've used all three services to get around when needed. Taxi is actually by far the easiest to get a ride on. The reason is being on the correct side of the street and for the car to be traveling in the direction you're headed is crucial.
Grabbing a Lyft or Uber may commit a driver to having to turn around the block, which can take several minutes, and in that time, you could have hailed half a dozen taxis.