Having moved to both cities without really knowing much about them and not knowing a soul in either, I can say without a shadow of a doubt that I prefer NYC.
I am probably biased because I got lucky with my apartment, neighborhood, roommates, job, coworkers etc., the circumstances were completely different when I moved to each city, and I have admittedly not lived in NYC for very long, but I have yet to experience the stereotypes that I had prepared myself for. It just seems like NYC comes with all this baggage because people expect it to be the most incredible place on earth, and obviously it can't always be amazing. When you weigh it all up though, even though it can be shitty in some respects, NYC has soooooo much to offer that most other cities just can't.
It's a shame that there are so many snap judgements made about it and its inhabitants - obviously in a city of 8 million there are going to be a lot of jerks, but I have met some of the most open, accommodating and friendly people here.
I feel like London can occasionally be awesome, but is mostly pretty average with some slightly better and slightly crapper things about it. Overall I find it unwelcoming, claustrophobic and judgmental - but again, this is just in my experience of it.
Having said all this, I have only really lived in 3 places so I can only compare them.