With private pregnancy care you will see the same obstetrician for all of your visits. This allows you, and your partner to form a bond and trust with the person who will be responsible for the safe birth of your baby.
As a clinician, knowing your patient enables you to recognise changes (sometimes subtle) when they occur. This can lead to early detection, monitoring and interventions that may improve clinical outcomes.
In the public sector, you will often see a different clinician at each visit, and these visits may be few and far between. This can make it hard to establish a relationship and recognise changes or complications when they occur. A potential benefit is that you receive multiple different opinions on your care, however this can also be confusing and frustrating for patients.
Most public hospitals offer midwifery programs where you are assigned to a small team of midwives who will also deliver your baby. This promotes continuity of nursing care but is generally limited to low risk women. Also you may be delivered by a member of their team rather than a specific midwife.