My decision would be based on the school(s), personal budget, and children's abilities.
Not all private schools are better than public. Not all Christian academy's teach or exemplify truly Christian philosophy - especially when those who attend or sit on its Board engage in snobbery of word, deed or thought!
I have lived in communities where I believe my children would benefit socially, academically, philosophically and physically from attending a private Christian academy -- and I have seen other such institutions where I would much rather place my children in the public school system.
What is the academic philosophy of each school, what are their grade standards? What is their code of conduct and how do they enforce it?
Not a simple "yes" or "no" or "A" or "B" answer! :)