@stackjip:
At all three of the major prep programs in NYC, Mannes, MSM and Juilliard, the audition is to gain admission, they give theory and ear training exams for placement, but you get in based on an audition in front of a panel.
In terms of hierarchy the toughest admit is Juilliard’s pre college program on the whole, MSM is slightly less tough and Mannes is a bit below MSM (and keep in mind this is on average, and doesn’t necessarily mean one is better than the other). You will see teachers who teach at all three programs, so the level of teaching is pretty close (there are good teachers at all the schools, and some not so good ones, depending on the instrument/area).
Because Juilliard has the name it does (much like the college), it attracts very, very talented kids and they don’t admit a lot, so to get past pre screening on violin, for example, takes a lot (before pre screening, they would audition 130 kids for sometimes as few as 10 slots).
That doesn’t mean that MSM and Mannes are inferior or not worth going to, like anything else, it depends on the area the kid in interested in. I cannot speak for the Bassoon, but with violin there are great players going to both Mannes and MSM, and there are top notch teachers at both places, and like with conservatory, the teacher is going to be important. Yeah, there are cultural differences, on violin at Juilliard and to a certain extent at MSM you will see kids in their teens who already are soloing with major orchestras, you won’t necessarily see that caliber of kid at Mannes. All three offer ensemble training (chamber, orchestra), because the range of players is wider at MSM and Mannes, the orchestra and chamber experience may be a bit lower level than Juilliard, but that likely isn’t going to matter much for a student.
Put it this way, kids from all three programs end up going into music, and getting into high level conservatories and music schools, so the level of preparation is there, it is really going to depend on the teacher being a fit and being a strong teacher who works well for the child. I believe all three programs would require her to choose a principal instrument, she may be able to minor on the second one, but from what I saw (and it is only that) kids generally end up choosing an instrument and staying with that ( I saw a girl at Juilliard who was double majoring on Cello and Piano and was at an incredible level on both, but that is pretty rare).
If it were me, I would focus on the teacher on the principal instrument and then after that, decide whether you like the culture. Despite the popular perception, neither of the 3 schools are cutthroat, and what usually happens is kids find others like themselves within the schools. It also depends on what drives the student, if they are driven forward by being around kids where many of them are more advanced than they are, then MSM might have the edge given the general level of playing there, Mannes might be a bit more laid back than MSM and that might suit others.