I personally went to a pre-K Catholic school and let me tell you, the stereotypes of Catholics being mean and all is completely untrue. I am Protestant, and they were very accepting of me, way more than the so-called Protestant public school system, which is elitist, and wanted to keep blacks and other races out, in a way to advance their corporatist imperialist agenda. Catholic schools teacher unbiased material. My only recommendation is a choice to have a uniform or wear watch you want, as long as it's not showy or indecent. Otherwise parochial education is better. Much nicer people, and a lack of the KKK nature of public schools.
What is taught in religious education is far more important than anything else you teach a child in school. When you teach a child to read it will service them for the rest of their life. When you teach the religion that it will service them for eternity.
There is no more evidence for theories like evolution than there is for religion, so I don't see why people think they have a right to call it fact when it's just popular science and unproven.
Unlike with public schooling, religious education does not have to meet the state standards and can indoctrinate children in unproven, non-factual beliefs regarding history and science.
While one could select specific schools to show one of either type is better than another of the opposite, in general parochial schooling has more drawbacks than advantages- particularly once that student enters college or the real world.
Private schools need not tolerate students that cost more to educate while public schools take everyone. The most important component in education is the individual student, a motivated student will do well wherever they go to school and many private schools meet their needs but public schools allow all students a broader experience and better prepare them to be members of a democratic society.