I believe that the question is not what is the difference between schools, but where your kid belongs. We live in OK public school district. However, my D. was in private k-8 for the simple reason that no public would take her as her birthday was 5 days earlier the deadline. We sent D… early to the kindergarten to one of only 2 privates that accepted her despite of her “low” readiness score. Anyway, her 8th grade class in the tiny private middle school had only 4 kids total. Our public HSs have about 500 kids in their class. We thought that sending our kid from the class of 4 to the class of 500 would result in great social shock and may be affecting our D’s future negatively.
Instead, we sent her to the private HS that happened to be #2 among privates in our state. Sending our D. to the school with 33 kids in class was much better fit or our D based on her background.
Question of which school is better than another has to be in connection to which school is better for a specific child.
In regard to the low readiness test - good that we ignored any advies from “professionals”. Kid never had a single “B” in her entire academic career and is graduating from the Med. School in May. This test proven to be bogus assessment of “readiness”