I sent my kids to Catholic schools for the most part, but they still had lay teachers and some of the books were ones used in public schools. Some teachers were better than others and as my five went through the system, the great teachers would be gone by the time my youngest was there :(
Individual teachers really determine the worth of the school year for the most part but there was always some decent content in the classes, and no discipline problems.
I homeschooled for a year. The curricula was the best I have ever seen. I even incorporated Latin I. It was made so easy to teach, I was amazed. Translating long sentences by the end of the year. Only had school 3 hours—five days a week but read great literature and did extravagant oil paintings, paper mache projects, diagramming sentences, etc.
Now adays I would NEVER send my child to a public school nor most private schools. I would homeschool. The moral relativism and revisionist history is too pervasive.
My two older sons went to a private Christian school. Pretty much what you described... They used public school text books, too. Basically, we paid LOTS of money for an ok education.
Home schooling is a gift from God for us. My son, (and I) are learning Latin, too! Classical education enables you to form a solid foundation.. a “peg” on which to hang future information (and to use to form future logic).