I haven't been to NYC but I get the impression it's much bigger, geographically, than London. Actually, what people call "London" is an accumulation of a number of separate towns / boroughs - The City (square mile), Kensington, Chelsea and Fulham, Westminster, Hackney, Tower Hamlets, Islington, Shoreditch, etc. All have their own demographics and good/bad bits but the bad bits are rather more obvious these days than I can remember when I first got here.
The austerity measures in the UK have impacted most towns and cities. I was in Manchester for the first time in quite a while the other week (that's pretty-much where I'm from, originally) and I was saddened to see the number of lost looking people wandering the streets and, many of them, begging. This is the 21st century and that sort of stuff was meant to have been consigned to Victorian history books. Very little civic pride - but they can always find money to build new shopping centres....
Unfortunately, governments just keep on demonstrating they can't govern and banks, collectively, screw up entire economies to the point where the government has to step in and bail them out and then tell the rest of us that we have to tighten our belts and accept swingeing cuts to education, health care and public services, generally. The current crop of UK teenagers is the first generation in umpteen centuries that will have a worse standard of living than their parents - which may be about the saddest prediction I've ever heard.