I don’t think it there is much academic difference in lower elementary. AAP in those grades is all that much different.

It matters more in later elementary and definitely by middle school. IMO parochial schools aren’t able to accommodate teaching up more than maybe one grade generally. Many of the k-8 schools don’t even offer math beyond Alg I. So if your 6th (or 7th) grader is ready and able to take Alg I, what will they do for 7/8th? Same for English in the upper graders. They will hit a ceiling to what the school can offer well before the highest grade there

If I was Catholic and we could afford catholic school, we would probably go that route even if our kid(s) got into AAP. I said this on a different thread - AAP is not like a mini private school inside of FCPS. You still have to deal with all the same BS. There will still be disruptive kids with no discipline, there will still be awful substitutes, and art and PE only once a week and just one 30 minute recess.

A good friend chose parochial over AAP because the parochial school taught in a more “classic” way that she felt her kid needed. More memorization and repetition, and less project-based and self-directed learning. Neither approach being better or worse, just different. They are not particularly religious and haven’t found that to be an issue. The public school actually had smaller class sizes so check in that with both schools if it’s something you’ll factor in. Her kid is thriving in parochial school but now they’re wrestling with where he will go for high school since their school only goes to 8th grade and the Catholic high school is far away. Something to consider.