400 years? That's all?
Apparently London is rather more efficient, which is implied by saying NY is the worst by large margin. It's also been there rather longer. William the conqueror built the tower shortly after 1066 and the Romans called it Londinium.
So, age is no excuse. In fact, N.Y. Is clearly planned with it's nice regular grid of streets. Actually they were going to do that in1666 after a large amount of London burned to the ground but the residents had other ideas and rebuilt very very fast when they heard about a pending government land grab.
Anyway, we have lots of stuff. A good underground rail network, a decent surface rail network (with really awful operators, Fuck you southern), lots of busses, many of them hybrid, river buses, congestion control and so on.
Southwark also has a massive recycling facility (worth a visit on open days if you like vast and complex machines). Recycling and trash get collected only on alternate weeks. Anything even vaguely compostable gets collected weekly and goes into a giant municipal composted which can deal with near, bones, fat and all the things you don't want at home.
It's not perfect, but it shows you can lower the impact of large and old cities.