Bart closes at midnight and has four stops in the heart of SF. NY has an OK metro but if you want to go cross-town, better just walk. I've spent time in NYC and lived in SF, Zurich, Berlin, Prague and London. Europe destroys on this topic. A huge percentage of people in Europe, like myself, don't own cars simply because we don't have to.
Saying it's no contest is a huge exaggeration. I won't argue that BART/MUNI is better than other transit systems, but I still get around without a car.
That said, the fact that transit closes in London and Paris while New York doesn't is a major advantage. It's actually precisely the reason why I have been able to not take a taxi or have to walk home in the early morning. And in NYC, a lot of people don't own cars because they don't have to either.
And a lot of people in NYC don't have cars simply because they can't afford to park them, not because available mass transit makes them unnecessary.