I went private with dd but have gone public this time. I couldn't justify the expense now the rebate has changed. You def only get back a small amount from your management fee from Medicare no matter if you get to the safetynet or not.
If your baby is sick they will get care no matter if you are private or public. Most private hossies have small SCN and often can't take babies below a certain gestation (where I had dd it was 36 weeks) so they sometimes go to the public hospitals anyway.
Saying that tho I'm not going to my local public hospital cause their system of general ante natal care isn't great,(no appointment time, busy clinic etc) so am going a bit further out and doing shared care. I'm not high risk tho, if I was I'd consider going back to my ob.
A gf of mine was high had all her appointments, scans etc thru the public fetal maternal unit which was the best place for her because they only deal with high risk so see it all so to speak.
Public it is harder to ask for inductions and c/s, they make you work for it a little bit. That is the advantage of going private.
You have to feel comfortable with whatever you decide..good luck