While I would certainly like to see an end of the year tournament of public v. MIAA schools or more games played between the two, it is just not a fair comparison. Private schools can recruit, while public schools must take who ever is in their district. Private schools can get unlimited donations from boosters or private donors, while public schools are capped and have restrictions of the amount of money they can accept. Title IX comes into play for public schools and not for all male private schools.
Advantage private schools on a consistent basis. Of course there are exceptions...