Families weighing private school often forget the alternative has a price too: a home in a strong public district costs more. But most of that premium comes back when you sell, so the real cost of buying up is the carrying cost, the mortgage interest, property tax, and the return you give up on a bigger down payment, minus the extra appreciation. This weighs that against tuition, for however many kids you have.
The two numbers are not the same kind of thing, and that is the point. Tuition is money spent and gone. The housing premium is mostly money moved into an asset you get back, so only its carrying cost is truly spent. When the housing cost is lower, buying into a strong public district is the cheaper route to a good school. When tuition is lower, or you have one kid for a few years, private can win.
Two things this cannot price: whether the specific public school actually fits your kid, and the value of a private school's program. Use the rankings, pathways, and school pages to judge the first, and the private directory for the second.