NYC subway is complete trash, it's one of the most depressing aspects of living in New York. Any impressiveness that comes from it is not from the system itself but rather the density of the surface above it. You feel like you just got from one side of the city to another quickly, but that was in spite of the crappy subway system; it was because so much is crammed within 2 miles above you!
I think vehicular traffic is far and away the most depressing aspect of NYC. All of the noise, pollution, bad attitudes, and danger to pedestrians and cyclists and it's not even close to being a timely and efficient way to get around. The subway is a damn miracle compared to any other current form of surface transportation.
New York is compared to London and Hong Kong. That's why they're called the Big Three.
I'll be the first one to talk at length about the many problems of the MTA and the effects on New York public transit, but to be honest, it still comes out ahead of London. It's absurdly expensive due to corruption, and there's no excuse for amount of money the MTA spends for the outcomes it delivers on, but the picture you're painting isn't accurate either.
Despite how bad it is, the NYC subway is still the best public transit system in the US, so Americans are infatuated with it, especially those who never user other subway systems.
So New Yorkers are like "BART sucks, my subway is way better, itś amazing", while the rest of the world is like "oh, you have shitty dirty metal boxes that break down all the time and you call it public transit, how cute..."