In general, yes. But that is due in part to most private schools being college prep in focus and not comprehensive by necessity as are most public schools. You won't find shop classes in most private schools. You won't find the same percentage of kids with IEPs in private schools as you do in public schools.
You do use the words "in general," which is good because we should be careful of absolutes. For example, Loyola offers five foreign languages, and Lake Forest Academy offers four. Prospect High School, a public school with 200 more kids than Loyola and 1,700 more than Lake Forest Academy, offers three foreign languages.
I think it is worth noting in this discussion that, in pretty much all faith based private schools, there are entire academic departments devoted to religious studies. Depending on the school, faith based private school students are required to take upwards of four years of those classes. There are a relative handful of public schools in this state that offer religious studies coursework, but only as electives housed in a social studies department.