I moved from Ottawa to Hong Kong. Supposedly the former is relatively cheap, while the latter is relatively expensive. That's according to what everyone, including bodies that study this sorta thing, say. But the truth isn't nearly as clear cut as it seems. There are four factors you need to understand if you consider moving to Hong Kong (this likely applies to a number of large cities)
First, housing is going to be your biggest expense. In Hong Kong, you can expect to pay about 25% of your income for a comparatively small apartment. I live in a 700sqft 1 bedroom apartment and pay approximately 25% more than I did in Ottawa for a single family house which was 4x bigger (plus it had a yard..and a garage...).
On the flip side, wiki describes Hong Kong taxes as being a tax haven. Income tax is fixed at 17%, there are no sales tax, and no capital gains taxes. Its also worth pointing out that if your employee supports it (and most large employers do), you can get a pretty significant tax break on your housing cost. Surprisingly, most cost of living indexes don't take into account tax rate!.
At this point there are a couple things to consider. First, this is all relative to the current housing and tax situation where you currently live (if you live in Tokyo, Hong Kong housing might seem cheap). Second, citizen's of certain countries (notably the US if I understand correctly), must continue to pay taxes in their original country - hence negating any tax breaks. (Canadian citizen's are taxed based on residency, and thus can avoid paying Canadian taxes, provided they can prove they aren't a resident of Canada - which isn't as easy as simply not living in Canada).
I don't know how it actually ends up, but lets assume the expensive housing is balanced out by the low taxes. There's a third and final factor to consider: how you live. Hong Kong lets you live however you want. You can eat at a different expensive restaurant every day of the year, and you can buy all types of brands that you are familiar with. You can eat the foods that you've always eaten, and wear the clothes that you've always worn - but it'll cost you. On the flip side, you can embrace local products and live cheaper than you did back home. For the truly global brands (IKEA, McDonalds, ...), things are normally cheaper in Hong Kong (both in terms of actual price +++ the lack of sales tax) - but in most cases, what you think is a global brand (say Kellogg or Procter and Gamble), probably isn't.
A forth, lesser, point to consider is that Hong Kong public transportation is excellent. 90% of all daily travel happens via public transportation (again, according to wiki). The point? No car payments/insurance/maintenance or gas. For most people, this will be a significant saving.
So that's that. Housing is expensive, taxes are low, and your willingness to embrace a new culture will likely decide whether moving to Hong Kong is noticeably cheaper or more expensive.