First, understand that these are high schools with prescriptive curricula where every student is taking some level of pretty much the same core courses every year, no majors or specialization. All of the schools you list are strong in all of your areas of concern. STEM vs. humanities is not a relevant tie-breaker in that pool.
Also, @Altras is correct about not topping out at any of them, and @Happytimes2001 is correct that a kid who loves one thing might end up loving something else more later. These are unformed youngsters primed to benefit from the breadth of what all of these boarding schools will expose them to. What comes out will look vastly different from what goes in; that’s the nature of youth and education. It’s a powerful combination. I think our son is the most extreme example of this. He entered Choate interested in applying to film programs. He ended up an EE at a service academy. As I always say here: Kids. Can’t control 'em.