Sweden's is an odd hybrid, because it has private schools, but they're heavily regulated: they must charge exactly what every other school charges (which is the value of the school vouchers), and must teach the national curriculum. Schools aren't allowed to charge extra on top of the voucher, so there's no price discrimination at all; in effect they're government subcontractors providing alternate implementations of the standardized product.

Hmm. So, it seem the definitions of public and private are skewing the ability to compare apples to apples?

There appears to be no way to "normalize" the data.