Let me start this off by saying that I have attended private school my whole life. I do not really know what public school is like, so I do not know if I could accurately provide answers or an outlook for that side of the argument. However, I can give my opinion, so that is what I am going to do.
I believe that private schools are fantastic. They provide small class sizes, more personalized attention, and generally have better facilities. They can also be very expensive and not have a whole lot of diversity.
Public schools on the other hand generally tend to have a lot of diversity, have more programs (like more options in majors/classes/extracurriculars/etc), but can also be overcrowded and underfunded.
My mom has worked as a teacher and a public school administrator for her entire professional career, and always tells me about how crazy it gets. She talks about all the budget cuts (which private schools are not affected by), which have really affected teachers and obviously students. These budget cuts have caused bigger classroom sizes, so that teachers can no longer have that connection and one-on-one time with students that they could have had before. This, many times, causes the students to not do well on exams and in school in general.
However, there is no clear answer as to which type of schooling is better. Private and public schools both have their positive and negatives, so it is up to the student and their family to decide which one is the right fit for them.
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Image 1: http://giphy.com/gifs/season-4-the-simpsons-4×12-l2Je95M0e46BHkuHK
Image 2: http://media.mlive.com/kzgazette/opinion_impact/photo/private-vs-publicpng-d829d72fcea4f62c.png