TO clear this up.
HKG has a government funded public health system that is essentially free to all residents. Also there is a system of very expensive private hospitals.
Both systems provide good quality care - however the private hospitals will do a song and a dance and give you a private room with nice food etc etc - the public ones wont. So really its up to you if you want to spend lots of cash when you break your leg or not.
If your wife is having a baby - she can do it in a public hospital ward for next to nothing - or in a private hospital room for 100 000 HKG $.
Most doctors work at several different hospitals. So quality of care is not necessarily better or worse at different hospitals. However if you need some sort of complex procedure ( not emergency ) then you might wait a longer time before a public hospital can do it for you - while the private one should be able to take you right away. Like anywhere - the more you pay the more prompt the service!
If you work for CX you have access to both - at least the HKG based guys do - I am not sure about guys based outside HKG since they won't have residence and a HKG ID?? They will be covered by CX's worldwide emergency insurance anyway though.