Manhattan is not that big a drinking town, actually. Whenever I visit London and see the drunk kids on the sidewalk in the west end, I’m always reminded of how unrowdy Manhattan is on a Friday or Saturday night. So public drinking is not really a huge problem at all. Public urination among the homeless? That’s a problem!
Actually yes Manhattan is big on drinking, the difference is the bar closing times. In NYC they close at 4am while in England I believe it's 11pm
In my younger drinking days I lived in places where the bars closed at 1am - 4am. In places like NYC where the bars close at 4am, people generally stay at the bars and then slowly calmly filter out and go home over time.
In places where they close early, everyone leaves the bars at the same time and they all hit the street at once and they continue drinking on outside or go to after hours parties.
So early bar closing times tend to have the opposite effect.