I attended public school from k-7, private school from 8-11, and public school again for 12th. There are ups and downs for both but I really do think that having a combination of experiences with schooling is beneficial. I don't remember much about going to public grade school except that the whole focus seemed to be on getting us ready for exactly what was going to be on the statewide tests and nothing else. Schools get funding based on test results so as long as they educated us on the contents of the test they neglected most other things When I transferred to private school, two things became immediately apparent to me. A) The kids that had spent their lives in private school seemed very naive and younger than their age to me and B) They were also a heck of a lot smarter than me even though I had been a straight A student.
I believe that public school better prepared me for the big bad world. The quasi altruistic society that they try to teach you is out there in private school is a joke You can't be gracious and understanding all your life out in the real world. It just doesn't work like that! Sure, if EVERYONE in the outside world was a real Christian then it might work like that, but it just doesn't. The kids who had ALWAYS attended private school didn't seem to have any experience at all with mean bosses/mean teachers/mean anything. I don't feel that they are able to leave school with enough preparation for what is out there. You can't protect yourself if you don't know what there is to protect yourself from! Does that make sense?
On the flip side, the curriculum and quality of classes was VASTLY superior in the private school. I started out in the same classes as the rest of the 8th graders but I attribute that to being ahead of most of my public school peers. Despite being ahead of my public school peers, I still had to work harder to catch up to my private school school peers. The classes were based on TEACHING us things rather than getting us ready to take a standardized test. The teachers were all very intelligent, highly qualified, and willing to give of their free time to help us out if we asked for it. Most of the student body wanted to learn and those who went against the grain and disrupted classes were usually the ones that people looked down on. Been there, done that Even though I was one of those people for a while I still managed to keep and exceptional GPA
For my senior year, I transferred back to public school... There was a big element of "culture shock" because I was suddenly surrounded by C students who thought that having a C was OK and Average and also students with Ds and Fs who just didn't give a crap. When I compared the curriculum of the public school to my private school curriculum's it was kind of a joke... I remember looking over my senior syllabus' and pointing out how many years prior to that year I had learned that information. I don't think that I learned a single new thing my senior year but I guess the review of private school 9th and 10th grade classes was beneficial in some way
Again on the flip side of THAT was that I was able to take an AP class at my public school that wasn't available at my private school. Most of the same material was covered in private school but was considered basic rather than advanced. Because I was able to take the class labeled an "AP" class I was able to take the AP test (aced it) and was able to get several classes worth of college credit for it.

To sum it all up, there are definitely benefits to both but I definitely recommend a mix of both.