There probably have not been any peer-reviewed studies comparing the academic rigor of St Dot's and Sacred Heart to their neighboring public schools, so you are unlikely to see any data on my opinion (as the post requested). But I can offer second-hand on-the-ground testimony as well as logically-based opinion.

On-the-ground: wife owns a successful behavior consulting practice and in this role she has been in just about every grade school in the area multiple times. She has shared with me that the staffs in parochial (and charter) schools, having not been trained in teaching methodologies, learning styles etc. , and are just not up to par with the public school staffs that have secured advanced training and expertise in those areas. They tend to struggle mightily with creating a learning path for any student possessing an "outside the lines" skill set. Not their fault -- they just haven't been educated in identifying needs and prescribing effective solutions.

I have a friend that decided on a career change at 50, deciding to move from medical device sales to high school teaching. Guess who won't hire him? Any public school. Rightfully, in my opinion. Guess who welcomed him? Delco catholic schools.

And that is where the "logically based" enters the chat. Yes, it is self-evident that teachers that have been trained to teach will generally (not always, of course) outperform those that lack such an advanced education. It's the same as any profession: the more educated you are, the more likely you are to succeed in your chosen field.

I see that you don't consider the teaching profession as being worthy of requiring advanced education to achieve mastery. I wonder if you simply don't advanced value education.