My sister is a midwife with several years experience now, South Australia. Aunty also a highly experienced midwife and pediatric nurse who has worked everywhere (she gets good money doing temp work). I know lots of midwives! When they all do their training they get sent around the state to most of the public hospitals, and also do a lot of work in most of the privates. Midwives tend to know a lot of midwives and hear what everything is like everywhere.
They all unanimously agree, all the time, that Public is the way to go. Pretty much the only reason to pick Private is if you want your own hotel room. That's about it. Damn expensive hotel room.
-Public is much better regulated. Midwives and doctors all conform to the latest cutting edge standards of care informed by the best science available. My sister literally is made to read Nature and Lancet papers, and then the new piece of policy that comes out from it (well not really made, she loves it!). In private its all up to the individual doctors and hospitals what they do. They can be years behind in some things in best practice.
-Yes, you won't have the same midwife for the entirety of the stay, but why would you want to? You could land a crap one!
-If anything goes wrong, its always off to the big public hospitals which have all the specialists on tap.
-Modern best practice is to get parents and babies home earlier rather than later, assuming everything is fine. It is better for healthy mothers and babies to be at home. Public system will keep you in if there is an issue. Most of the time in Private you are paying for a room for a few days that you don't really need. Go home and sleep in your own bed and be in your own environment :-)
-If something is really wrong as I said they keep you in Public anyway. If you really need the help past visiting hours there are midwives there overnight, and sometimes they let fathers stay anyway, depends on the hospital.
-Public they send out a midwife for at least one visit after you go home-so if you need more advice you can get it. Also, you can call them up for phone advice too. For most people this is plenty.
-Shared rooms are little issue in a Public maternity ward. Usually its only two mothers to a room. You might be lucky and have no one. Its more likely a midwife is nearby. Trust me, after going through childbirth, your sense of privacy with strangers will all be shot out of the water! Sharing a room with another mother and baby is pretty tame compared to many many people coming in and starting at you for hours during birth. Heck, you'll probably make friends! My daughter's best friend is the girl that she shared her first room with, in hospital...