I have never delivered private but considering it this time. My choice is Baptist (paid the deposit before the two incidents reported in the news not the thread on this forum) but if money was no bar I would choose between Mathilda and Sanitarium even though I live on the Kowloon side. They are most accomodating to the mum's wishes. Getting from one end of HK to another is not such a big issue and first babies take a long time to come from the start of contractions.
If I were choosing between Baptist and Theresa, I would choose Baptist (I've read scary threads about Theresa also, and basically every single person in my office has delivered in Baptist and was happy). On the Kowloon side my choice would be between Baptist and Union. I would have chosen Union only because of the two incidents at Baptist reported this year.
However, if I had 100,000 or more, as I said I would be choosing between Mathilda and Sanitarium or failing that Canossa. I would pick Sanitarium because it would be closer to get to from Yau Ma Tei than Matilda but if I didn't get a booking at Sanitarium I'd be more than happy at Matilda. (I thought Lesliefu and Elle were talking about experiences at Matilda in their posts).
In terms of dealing with neo-natal emergencies, my understanding is that the public hospitals are the best equipped. However, if your fiance's pregnancy is smooth, I wouldn't make plans for neo-natal emergencies. Worst case, the baby can be transferred to public. If you can afford it, let her have the most pampered delivery she can as well as good care - and that is what you'll get at Matilda/Sanitarium.
I smiled at your use of the term "vulnerable". It's childbirth not rocket science. Things do sometimes go wrong but most of the time, everything is fine. Don't be afraid.