I have lived in several major world cities. Moscow, St Petersburg, Warsaw, Cairo, Singapore, Shanghai.
I like London (was born here) for all its not inconsiderable downsides. And they are big ones -- overcrowding, expensive and shit housing, appalling traffic, unreliable and expensive transport, nightmarish schooling.
It is one of the most diverse places on the planet -- I find it more diverse than New York even. It offers those cultures' food and shopping experiences. The shopping is good (not for everything but all-round good). The stuff for children to do is just limitless. My husband remembers bored kicking around in Bristol as a teenager and thinks London is far better for children. Museums, restaurants, cafes and eateries, unusual shops, clubs, sporting activities, scenery, diverse architecture, joie de vivre, atmosphere, history, theatres, film theatres etc etc. Without equal, I'd say.
I hate the wintry weather though. Sometimes I'd like to live in Madrid even though some Madrilenos are racist and call me guirre.