I have firsthand knowledge of both public schools and private schools. I attended Catholic school until high school, when I switched to the local public school.
At the 2 private schools I attended, parental involvement was much higher. Parents volunteered for various fund-raisers, attended Back to School nights to meet their children’s teachers, and genuinely cared about their children’s education (obviously, since they were spending quite a bit on it). At the public school, it was very much the opposite. The 2 public schools I attended were both much poorer schools on average (this was in the days of zoning, where you attended certain schools because of your location. They’ve since switched to allow students/parents more choices, so that the schools are more competitive). Poorer parents, for any number of reasons, put less effort into their children’s education. It may be a case of it not being a high priority, or it may be that they have to work several jobs to pay the bills, and don’t have the time to be more involved with their children’s education. Either way, parental involvement is a large factor when considering a school’s performance.
On top of that, the curriculum at the private schools I attended was more advanced in many ways. I read some books in middle school that public school students don’t read until high school, for example, two of Shakespeare’s plays. Also, the private schools did not rely on students’ standardized test scores for funding, so my teachers spent no time in class teaching to those tests. We still took standardized tests, but merely to measure our individual progress, not to ensure our school received more funding. In the public schools, the standardized tests were so important to funding, teachers spent weeks of class time teaching to the tests, which are all very basic, so that left little time to get into more advanced areas.
Also, my classes were much smaller (sometimes half the size) in private school, so that the teachers could focus on children who were struggling without having to dumb down their classes. With math classes, it went even further- they split the students into 3 different levels so that the more advanced kids got algebra in 6th grade and didn’t have to waste their time reviewing basic arithmetic with the less mathematically-inclined. I’m not much of a math person, but grasp it well enough that I got to take classes my freshman year (at the public school) that consisted entirely of seniors. If I had been in a public middle school I am sure I would not have been so advanced (because I’m not really a “math person” but my advanced math classes in middle school consisted of only 10 people, so I got plenty of individual help).
Discipline was not really an issue at the private schools at all. We did have one or two trouble-makers, but the smaller classes helped teachers because they didn’t have to deal with 4 or 5 troublemakers at once, usually only 1 or 2. Also, the parental involvement mattered. At the private school, teachers were quick to call a parent-teacher conferece if necessary (it didn’t often escalate to that point, however). And a parent who’s paying more than a grand a year to educate their kids is not going to be happy if they hear they got sent to the principle twice this month. At the public schools, I never heard the teachers even threaten calling someone’s parents. I’m sure if they tried, they would have gotten laughed at. In many cases, I doubt the parents would have cared or shown up.
The type of disruption differed greatly. At the Catholic schools, it was likely to be someone showing up late to class, passing notes, or having their shirt untucked. At the public schools, it could be anywhere from drug use/smoking in the bathrooms, to threatening the teacher, to fist-fights in the hallways. My freshman year, a fight broke out near my locker and I was thrown up against the wall in the scuffle. In 9 years of private school, the closest I ever saw to a fight was when I smacked a kid for making fun of me in the second grade. I actually saw the SRO (the cop on campus) get his ass kicked in a particularly brutal fight at one of the public schools.
Also, WRT to differences between public schools, the quality of education varies widely. In my county, all of the best public schools (based on test scores) are in the wealthier communities. They tend to have better technology, smaller classes, and attract more/better teachers. Who can blame than, would you rather teach spoiled rich kids or the kids that deal drugs and bring weapons to school?