When you factor in all your out of pocket antenatal costs, any gaps for scans and bloods, hospital excess, gaps for paed or anaesthetiest fees, it would be feasable to say you will be out of pocket approx. $2-3000 going private. IMO about the best part of going private would be getting your own room at the hospital.
Never, ever assume private covers means you get your own room!

I had a great Ob for my 1st, a lovely man.....but I didn't need him