Perception bias is a hell of a drug.

And most tourists from the UK or elsewhere, tend to stick to, well, touristy areas. Politicians tell cops to do more in those areas to keep them "clean" for the tourists.

So i suspect its about what neighborhoods youre thinking of in London, vs which ones you visited in NYC.

That said: the media loves to play up fear, and the homeless cause some people fear (they can be unstable, and unstable people can be dangerous) so the media will happily overblow a homeless situation to get clicks