I think we can agree that English is the lingua franca? This automatically renders any place which isn't English speaking less attractive to most people.
So out of the big cities we're left with London, New York, maybe Dubai and Hong Kong. I've lived in and arranged relocations for clients to all of these cities.
Out of these Dubai has a really unpleasant climate for half of the year, the rest are mostly okay.
Only NYC and London have reasonably available high end real estate, in HK an Dubai the quality of finishing tends to be really shit no matter how high end you go.
Schools? NYC and London are your only options if you want your kids to have the best education, London definitely edges ahead here and is reasonably close to top schools like Le Rosey.
Restaurants? Dubai is out, the rest are fairly even.
Demographics? If you're not Chinese you'll have an increasingly difficult time in HK, especially with the recent developments. The other cities are incredibly diverse.
Stability? HK is out, NYC will seem iffy to many thanks to the increasing polarization in American politics. Dubai's long term prospects remain to be seen, but despite Brexit UK seems more than okay.
Safety? Dubai and HK are incredibly safe as long as you don't upset the government. London is still much safer than NYC.
Location? Dubai and London win here. DXB and London are both extremely convenient air travel hubs. For most of the world NYC is far. HKG isn't great unless you're coming from Asia.
I think in the end for most of the ultra rich considering moving abroad it'll be a choice between NYC and London. Unless your family already holds US passports, odds are London is the better destination.