Here's a study done in Ontario, reporting on home birth and hospital births in low-risk women. In this study, both are attended by midwives, which, in Canada, are like AUS private midwives.

The report found that the outcomes in maternal and infant deaths were the same for home and hospital, and that the intervention and complication rate at home were much lower.

http://www.aom.on.ca/files/Communica...on_Sept_09.pdf