One of the biggest differences in these types of cities is parking is very limited or located underground, the buildings push very close to the streets, there's no excess road or empty front yards, and the buildings are mixed retail/residential.
Those things make for consistently more livable environments. There's no long trek across an empty parking lot and a big lawn just to get from point A to point B.
The result is it doesn't feel nearly as dense as it actually is.
This is in contrast to Hong Kong, São Paulo, and other cities that achieve density through high-rise buildings. You're intimately aware you're in a big city when you're in the built-up cores of these.
Also, I think it's very unlikely that NYC would be where it is had they restricted buildings to 5-7 stories. As it is they don't have enough density.
Ultimately, NIMBYism and these sorts of height restrictions are a result of the city deciding that it doesn't want new people moving in past a certain point. I won't moralize that choice, but it is certainly different than the set of choices that led to a city like New York becoming so special.