There are 2 primary reasons why selective schools like high yield rates. One is bragging rights/rankings. If you have a high yield rate, it implies that the school is more desirable over others and is factored into some of the ranking formulas. This is where it is argued that ED is being used as a form of manipulation to inflate yield thereby increasing perceptions of desirability and boosting rankings (see UChicago). EA on the other hand does not mandate matriculation and the higher yield is more representative of that school being a true first choice.
The more institutionally sound reason for wanting high yield is that the selective schools want to assemble "ideal" classes which have so many "round" kids, so many "spikey" kids of varying interests and talents, so many artistic/musical kids, so many STEM kids, so many URMs, so many legacies, etc... It's easier to assemble a tailored class when it is more predictable that a high percentage of students admitted will matriculate. In the ideal world, AO's probably don't mind that the yield of accepted students be slightly lower than the desired class size so that they can fill out the holes from the waitlist.
If your sons don't feel challenged at their current school and are the ones who want to go to Pingry, that would be a major, probably deciding, factor for your consideration. Then that would be a decision based on what you, your wife and your sons feel is best for their longer term success and happiness.
Who needs Europe when you can go to NYC and emerge in a "new country" just a couple of subway stops from the one you entered, lol.
@IxnayBob , that is quite an interesting role reversal of private (diverse) vs. public (less diverse), although I get it based on the neighborhoods you mentioned -- we had many friends and acquaintances from your and @ArdenNJ's neck of the woods back when I worked in the City.
I think that just illustrates how personal and fact specific the situation is for parents considering the best environment to place their kids for school. Each kid has different strengths, weaknesses and levers of motivation and each school has its own pluses and minuses. I guess there are certain generalities we can apply to most top notch private schools (more focused attention, more personalized guidance department with better access and insight to top college AO's) and large public high schools (less resources per student, greater diversity of achievement levels/motivations of students), but for the resources and opportunities that matter for your kid, the situation may be the reverse.
Another factor that will drive families' choices are their priorities. What is the relative importance of getting the best/most advanced academic education in high school, gaining admission to a "top 10" school, vs. things like gaining better socialization skills, including empathy, and having a relatively carefree/low stress high school experience. Finances are of course another issue as well. What opportunities are forfeited in order to pay for private school tuition and how does that otherwise strain the family as a whole.
@ArdenNJ , we have pm'd about related issues before, for my wife and me, we have always felt that it was important for our kids to know the "real world" and have exposure to kids and families of very different stripes. We were confident enough in their smarts that they would pick up whatever "technical" book knowledge they needed as they went along. Rather than send our kids to the district's magnet IB program (or to a private prep school), where they would be in a "bubble", we felt our neighborhood HS (where all their friends went) which had a full panoply of AP courses was a better fit. Maybe they would only have taken AP Calculus AB by senior year, but if they were really interested in more advanced mathematics, there were plenty of grad students at the local university who offered tutoring services. Maybe the magnet school sends half a dozen grads each year to highly selective schools and our school might send 1 or 2 with most of the top students going to the state flagship, but we did not think any opportunities would be closed to them. In the meantime, our kids went to school with their friends, played at a high level in the sports that had been playing since they were 8, and got to know and make friends across the entire socioeconomic and racial spectrums. In fact, our school went from majority white to majority nonwhite over the past half dozen years. My wife and I think our kids are better prepared for the real world (and probably better people) for having gone down this path. Maybe we were just lucky, but they also ended up at top colleges that fit them.
You may be tempted to look at admissions for selective colleges at the 2 schools and conclude that the private school is superior because even though it is half the size, many more of its students matriculated to top schools than the public school. It's obviously a lot more complicated because the private school is already selective in its students and what are the probabilities of your boys (if I remember correctly) making the top 20 there vs the top 1% of the public school.
I, however, would approach the question from a different angle. I would ask which school is a better fit for your boys -- where are they going to be happier and more motivated to learn? Are there materially different resources and opportunities (academic and extracurricular) in their areas of interest? Where are their friends going (assuming these are friends that are positive influences)? Have you included your sons in a discussion of their preferences? Assuming finances are manageable, if your boys are more likely to thrive at one school vs another, choose that one. It's not as if the public school is a troubled school and rarely sends students to top schools -- in fact it sent quite a few to the top schools.