This is where it gets tough,your S has some darn good choices, and this is where the numbers stop meaning as much, the analytics, and the gut comes in. For example, I wouldn’t use a given student as in indication of playing level, keep in mind that even at the best programs there may be students who seem, well, not so great. It is much better to see things like student performances and seeing many kids, to get an idea, or even if possible listen to the other kids auditioning to see the level.
My S auditioned at a grad program that is very, very high level, he sat in on a studio class of a very well respected and known teacher, and there was a girl playing there who he was shocked at how terrible some of her technique was, yet other kids in the class were mind blowing.
It isn’t that everyone at a U Mich or Juilliard (or even Curtis, I have seen kids on violin there that I really wondered how they got in, even to my ears that were not great), everyone is ‘the best’, the difference between schools IME is the relative numbers of kids playing at a top level, at a school like Rice or Juilliard or CIM or whatnot, on a given instrument there will be a lot more kids in that upper 5% then what you might see at a more ‘second tier’ school, so let’s say at “great school A” 5% of the violinists are at that top level, whereas as school B it may be a fraction of 1% (and these are totally hypothetical numbers, not real ones). The other big difference is the range of playing, at places like Juilliard et al, the range between the best players and the worst ones is going to be a lot smaller than in a less competitive program.
Likely, too, the playing level is probably more clustered in the top let’s say 25% (if there is any way to say “this is the level for the top 25% violinists”) at a top school, whereas the playing level at a less competitive school might be in the top 40% (again, purely for illustration purposes, when someone can scientifically evaluate violin level my son’s old teacher would track them down, shoot them and make sure their work never saw the light of day lol).
Obviously numbers come into play if something is financially undoable, but it is going to be a subconscious synthesis of teacher, program, school,location and how many great bars are within walking distance of the music school (well, okay, maybe the last one is only important if the kid is a descendent of PDQ Bach), and know that there is no science to it, no real ‘right answer’ like in Indiana Jones and the Last Crusade “You chose wisely” kind of thing, and that in choosing from multiple paths looking back what you often find (least with my S and with his UG choices), is that a choice he might think now would have been better for him 4 years ago would likely have had consequences (for example, had my son chosen Colburn, instead of the school he went to, he would not have had the experience he had with music theory, which is another big love of his, going there likely would have not allowed him to find/have that love). Plus there is the “road less travelled” syndrome, where down the road you took the road less travelled and it was great for whatever you choose:)