I can tell you why WE choose private school over public school but please realize I don't know your area and the strengths or weaknesses of any of your schools in your area.
I am a teacher and I taught in the public schools in our town. Our school district never has enough money for the things it needs, forget the stuff they would really like to have. So, for me, thinking that the teachers would have to make decisions based on how many copies they could make or how many crayons they could pass out bothered me.
I believe that the teachers in the public schools do a great job with the little they have and I know that my children would have learned how to read, write, and compute mathmatical sums just fine under that system. The problem is that in the public schools in my town, p.e., art, music, social studies, and science are rarely taught, if at all, in K through 3rd grade. I believe as a teacher that a well rounded education helps children learn to read and become better learners.
The private school that we go to provides all these subjects with specialized teachers whose passion it is to teach these subjects. This not only helps the quality of what is being taught, it gives their core teacher time to prep her lessons. In a public school the teacher that a child has often is expected to teach ALL the subjects regardless of their qualifications.
Our school is a Catholic school and we are Catholic. I wanted my child exposed to the values and teachings of this faith. I remember teaching Kindergarten in a public school the year I was pregnant with my first child. A little girl in the class 'flipped off' a little boy in the room. Fortunately, he did not know what this meant but it made me realize then that I did not want my children around other children whose parents may have more loose ideas of what was appropriate behavior.
With all this said, some public schools are great. If we lived in Portola Valley or Woodside (about an hour away), I would send my children to public schools. But we don't, and the public school we are assigned to do not live up to my expectations. ( I know this because I have friends whose children attend and hear stories).
Take a tour of the private schools in your area. Ask to visit the classrooms of the public schools. Ask if they have specialized teachers. If the classroom teacher is expected to teach all subjects, how often and what support is given to her/him. Ask to see the textbooks or equipment for each subject. Be curious and open to hear what each school has to say. You have to do what is right for your little boy and you will figure it out as you go. This is also not a decision that has to be a forever decision. You can change your mind.
The other (very minor) reason we choose private or public are the policies on attendance. Though a private school will let you know how important it is to attend, a public school can send nasty letters and follow up with truant officiers if a child is absent too often. Though my children are never tardy, we do like to take a family vacation once in a while. I don't want to have to hear about how the school is missing its ADA money (average daily attendance money) especially since my kids are above grade level.
I love the school that my children attend. Is it absolutely perfect? No. But it is always working to improve itself, its responsive to parental imput, and it teaches the whole child instead of just the core subjects.
Good luck!