Uber is 30% less than taxi's in SF. I think in NY it is also cheaper than taxi's. Your data might be a year behind, when it used to be more expensive.
And we haven't even started on surge pricing. Uber sells itself as cheaper than a taxi, but in many ways (in NYC) it is not.
It would be nice for Uber to publish some comparative data in this regard. But I think that's not their main pitch.
They now have a fare calculator for NYC athttps://www.uber.com/cities/new-york. It is pretty broken as all my addresses end up getting mapped to Brooklyn or Queens for some reason.
But for the prices I saw, UberX is 30-50% higher than yellow cab. So my 2x-3x estimate is certainly out of date.