In terms of being cosmopolitan, I would say NYC and London are very similar. IMO, getting around London by public tranport is much easier than in NYC, and both cities have their share of transport nightmares.
One cannot say London is England, just as one cannot say NYC is the US. Both cities are fast paced, etc, while going to other areas you will feel as if everything is moving slower, and in comes cases it is.
Living in a village is very different than living in London.
bvamin