I'm not sure what country you live in, but here in the States, Catholic schools have a couple good things going for them vis a vis the State-run schools.
First, the parents give a shit about their kids' education - no way around that. They have a vested interests (payment) in their own kids and in the school itself.
Second, they can reject "problem" kids, no matter how you define it, and get rid of them, if it benefits the school.
Third, they can impose discipline that cannot exist in the public school environment.
On paper, their teachers may not have the credentials required of State school teachers, but their relatively low pay often means that they take teaching as a vocation, rather than as a job.
My parochial school experience is generations out of date now, but when I graduated from a Catholic (Christian Brothers) HS in 1967, we had the highest rate of seniors going to college of any HS in the county, most 800 SAT scores, national merit scholars, etc. It wasn't even close.
And for the record, after 12 years of Catholic-school education, I never saw even a hint of the scandalous behavior that scourged that System over the years. The WORST that I even heard of was that a priest was later accused of an unwanted kiss bestowed on a Church Lady. For which he got fired.