our first bub is only 11 months old but we're pretty sure we are doing public for primary and private for high school.
I believe it is truly how much time you spend with your child reading, writing, helping with maths and incorporating maths into their lives that makes the difference in primary school. I reckon if the parents are willing to put in the time and effort with a young child it doesn't matter overly much which school they go to for primary.

but private for high school for the choice of subjects and more optional extras you get.

but if your choice school does p-12, then lucky you! no major upheaval when they change to high school!

Would you have much luck in getting your child into the high school classes if she didn't go primary there?