But if you have lived in S.F. and also New York, it's easy to see why someone would claim N.Y. is more diverse. I think it has a lot to do with embracing different ways of living. Its a pretty common joke how much conformity there is in the Bay in a basic workplace enviroment, ie. wear this flannel shirt, have 'x' opinion on social media, have 'x' political view.
New York isn't better or worse, but it feels like there is more variety in your day to day interactions with different types of people.