OK, here's some info for the UK, I can't imagine it will be that different.

Both hospitals and birth centres have birth pools, and you are only attended to by midwives unless there's a problem: the hospital will have an on-call Obs and the birth centre will have to transfer you. You pay for Obstetric care in Aus, so I don't know if the same is true for Obs turning up during birth for you, but both places are fairly similar for an ordinary birth.

The birth centre cannot give you an epidural - you'll need to go to a hospital for that.

The birth centre midwives will "know" you as you attend various appointments with them (2-3) before you give birth. The hospital midwives you may have never seen before. Depends if you're comfortable with that.

A straightforward birth, the hospital likes you in and out within the day. In a birth centre, they keep you there for 2-3 days if you want it and teach you how to breast-feed, how to change nappies, and there's someone to look after the baby if you want a shower.

The individual hospitals and birth centres will all have different rules and some won't allow water births, but you'll have to check with the hospitals in your area what they will and won't allow, but I hope some of that was helpful to you.