I agree it isn’t very telling to simply say that ‘free schools’ may perform better. Presumably parents removing kids from public school and placing them in private schools (US terms) can be said on average to not include the group of parents which don’t prioritize education. It would be surprising if such students didn’t perform on average better than less well supported students.
This doesn’t even include other factors like selective enrollment, different teaching mechanisms, difference class sizes, different cultures, different disciplinary procedures, and other possible factors.