I agree with all of this.There is no lesser or greater choice with schools there is only what is the best choice for my individual child.
You can look up myschools, naplan or any other range of data sets which gives you a whole lot of averages, but it doesn't mean anything when you are dealing with different children with different needs.
The biggest difference to a childs learning is the teacher. They come in good and bad at both public and private. Schools philosophies and teaching styles impact on quality teaching so this is important when making a choice. Class size makes a difference too but so does flexible learning spaces and it still depends on the learner on how effective this experience will be for them.
You get behaviour problems everywhere not just schools and especially not one type of schools. There's poorly behaved kids at every school and there's also poorly managed discipline policies at some too, private or public.
Your choice shouldn't be made on the type of school you want, but the individual child you have.
The only way to find out is to visit the school not visit any website with average statistics.