Third that the public hospitals are excellent, and that the private ones are basically hotels that send you to a public one if anything goes wrong...
However, in HK childbirth isn't "new age" friendly, it is technical, gynaecologist (not midwive) driven, geared to getting babies born safely with minimum danger to mother or child, not the experience. If you want home birth, shamans, water births etc. you are out of luck. One person's intervention and red tape is another person's necessary and mandated pre-natal check ups!