How are you assessing the quality of the programs at these schools?
Do you have access to college admissions data in a comparable format? A list of colleges students are admitted to is hard to compare to a list students actually attend. The admissions data can be skewed by a few super high achievers with many admits. The attend data can be skewed by family finances. Are the students at the public school getting admitted to top schools but attending at a lower rate because the parents are balking at the cost? I know at least one kid from our high school with an Ivy admit whose parents sent them to a state school because of the cost difference. Also know a few who might have been admitted but went for large merit scholarships. This seems obviously more likely to happen to kids whose parents also couldn’t or wouldn’t pay for the private school.
What about AP classes? Does either school place limits on AP enrollment that will significantly impact your kid’s education? How do the students perform on the AP exams, are there are reasonable fraction getting 5’s? This of course can be skewed if all students don’t take the exams, perhaps more likely to happen in a public school because the cost of those exams does add up. “I need a check for $460” “Uh do you really need to take all of those exams?”
One piece of data that should be easy to get is the number of National merit semifinalists and commended students. This can give you some rough idea of how many top students each program has. You might want to look at several years worth if the numbers aren’t large. Our small numbers bounce up and down quite a bit.
Have you spoken to parents, and to students, at each school? If you know students comparable to your own that is probably the most helpful.
Has your kid visited classes at each school?