I don't think it's as simple as Private or Public, but more looking at schools on their own merits and deciding if the benefits (of private) justify the fees etc.
This is what i was going to say.

I went to a public primary that was great, and 2 different catholic high schools- one was great, the other blah. You have to think about your child and their specific needs and what specific school will fit them best. e.g. one of my brothers was artistic and talented with his hands so the technical school was best for him. Another brother was intellectual (good at maths/science/english) and so a different school was best for him.