Let me pause and give you my credentials:
First, I come from a family of educators. My parents were both teachers - my father is a retired professor and my mother was a high school English teacher and librarian. On my father's side, both grandparents were life-long educators and my aunt is a retired teacher. All of this experience occurred in public schools and universities. My mother attended a Catholic grammar school for a bit as a child, but that's the extent of Catholic education in my family background.
As for me, my only exposure to Catholic education as a student was in high school (Knoxville Catholic, class of 78). Otherwise, it was public schools, a public university and a Divinity program in a private University (Vanderbilt). My husband is a product of public schools, K-12, and then Catholic colleges. My children have all gone to Catholic elementary schools. My 20-year old went to a Catholic high school, my 17-year old is in a public high school, and homeschooling is looking like a better and better option for the others.
I've taught religion in Catholic high schools for a total of 8 years, and my husband taught in a Jesuit high school for four.
So yeah, education is my interest, but I am, by no means an unquestioning apologist for Catholic schools.
A commenter pointed out below that, particularly in years past - the "golden age" of Catholic education in the mid-20th century, it was not necessarily true that Catholic schools were better than public. I don't think I said that - and I think the stories of huge classes taught by untrained nuns, nuns who could only attend school in the summers and therefore took twenty years to get a BA - bear that out. My impression is that before 30 years ago, there was much more of a balance in quality between the two.
And, for the most part, I think the present general superiority of Catholic education to public education is rooted, as researchers consistently point out, in shared values and community. Whenever you find that in a school, no matter what type - where ever you find parents, teachers and administrators on the same page and in a good, rather than adversarial relationship, you're going to find a good school. These days, you are more apt to find that in a private school than in a public school, for a number of reasons.
My own opinion - not gospel, just an opinion - is that for grammar school-aged Catholic children, Catholic schools or homeschooling are the best course. I think it's vital that for this age, learning and socialization take place within a values-saturated environment.
But high school???? That's a different story. We had a big blog discussion about this several months ago, and I don't want to bore with repetition, but I'll just say that when it comes to Catholic secondary education, parents should approach the question with "buyer beware" at the front of their minds.
First, it is impossible to maintain with a straight face that Catholic secondary education is generally superior to public secondary education. It's not, and it all depends on where you live and what the schools in your area are up to. If you have a bright kid, and the Catholic school in your area offers only a couple of AP courses and clearly doesn't value academics as much as it values other things - like sports, or maintaining the student body (read: tuition checks) by not challenging the dull-witted children of the wealthy - your child will be probably better off going to the public high school that has an IB program or a full load of AP programs or credit arrangements with local colleges and universities.
Same with other specialty programs - I know the Catholic school I taught at in Florida - small, struggling with identity - was badly hurt by the public school's system slow but relentless attempt to build up magnet programs, particularly in the arts and an IB program. A school of 200 with quite limited financial resources just can't compete with a school that can put on productions of musicals that are actually better than the touring shows that come through town for students interested in the arts, or with expensive labs that are really necessary to teach advanced science courses now.
But what about religion, you ask? Isn't that important?
Well, sure...but when you look at a Catholic high school, you have to look very carefully at how religion is expressed in the place - in the curriculum and in the school culture.
Let's put it this way: if a "Catholic" high school has a shoddy theology curriculum and does nothing to seriously combat the insult-soaked, materialistic, sexually-charged aspects of youth culture - if it turns a blind eye to parents hosting drinking parties for kids, if it lets atheletes rule the roost, if its dances appear no different than a night at a local club, if there is no emphasis on service - then you are better off putting your kids in a public school.
As I've said before, when kids see all kinds of nonsense protected by administrators who work under the Catholic banner, all for the sake of maintaining enrollment numbers and keeping the winning football coach, and when they see teachers and administrators refusing to actually be Catholic, the impression they take away from four years of that is that Catholic means "hypocrite" and they are more vulnerable than ever to the first seriously-minded, faith-filled, evangelical Christian they meet, who, quite rightly, asks them what faith is for, if not to guide the way you live?
Later: Frank Sheed on Catholic education. I was wrong - it wasn't about Catholic education in America, but about the quality of religious education in Catholic schools in England. But it's still pertinent.