Public is the way to go. Public hospitals have the capability to deal with all eventualities, not all private ones do.

I went public & I was allowed to labour far longer than any woman I know IRL who's given birth in a private hossy. I also got way more help with breastfeeding than they did too.

Anyone who thinks they are somehow better because they paid for their doctor & delivery & hossy stay is a snob. I paid my medicare levy through my tax ever since it was introduced & I was very glad that I could finally get to use the services I'd been paying for for so many years.