A city has to be more than just big to make it enjoyable. For me I like a mixture of parks and public spaces, good transport links, wide variety of leisure and working options, proximity to other interesting destinations, a nice climate, affordable housing, a sensible city hall/mayor, a good music scene, not being over dominated by tourists, an after hours culture, a sense of freedom, an undercurrent of vice, but with low serious crime, and a 24 hour availability of eating and drinking places. Being able to get by in English, no laws against drinking or being gay. Not being segregated along racial lines. Support for those who are homeless or in need of help.
London has a lot of this better than most places. New York is definitely more 24-hours sure, but lacks the proximity to Europe and has a less good public transport network. LA has way better climate most of the time, but lacks a lot of what NY and London have in vibrancy, public transport, historic architecture, an after hours scene etc. Plus it's full of cunts and not very multicultural. Amsterdam or Paris are arguably as multicultural, but smaller. Sydney is lovely with better weather, but doesn't enjoy the center of the world feel that London, or Europe generally has. They all have their pros and cons.
Regardless, all of them are way expensive to live in and can do you head in if you don't get out once in a while.