Charter schools are now in Canada as well, especially Alberta. As might be predicted, those that are strongly academically based get good scores on provincial tests, while the religion-sponsored fundamentalist schools get mediocre scores as a whole. Yhe good academic ones are quite expensive and the students are carefully selected. These schools, unfortunately, take money out of the public system - the old story of funding provided by the province depends on enrollment in the school district.
The separate school system (Catholic) is not really affected as yet; Catholic parents seem mostly happy with their separate schools (taxpayers specify which system, public or Catholic, gets their tax money). I am not familiar enough with the provisions for Muslim and Jewish schools.