If you are undecided, its definatley worth a tour as different hospitals will have different policies & models of care etc.

We have private insurance but decided to go public, mainly because my GP practises obstetrics, (so its not like I see a different doctor each time), and theres a large public hospital nearby.
I pay the gap for ultrasounds, and did have to pay $100 for antenatal classes - thats about all so far. All my GP appts & blood tests have been bulk billed.

My friend has done the private patient at public hospital thing - it means you can choose your OB & have a private room if one is available.

Private hospitals (well the bigger ones in the city) can tend to have big waiting lists so it pays to get in early.