Tigger Dad, thanks for sharing this and I hope we can hear what he chooses ultimately.
t First, these are great choices and the results of your son’s applications would seem to argue that all that stress was worth it. For the sake of others, I just want to say that there are cases where kids pursue one thing single-mindedly, even at the expense of academic rigor, and still get great results with elite colleges. It seems clear that TiggerDad’s son did all these things because he WANTED to, not “to get in.” And did VERY well. I just worry that some will read this post and think they need to have activities at this level and in this number to do well with admissions 
Both Williams and Princeton are great choices. They are very different, so the ultimate decisions may be easier than between two schools that are similar. I have relatives who went to both…
I go out to MassMOCA and the Clark Museum quite often. Williamstown is beautiful, surrounded by mountains, close to Vermont and NY, an area with some culture but also remote in some ways. Small, personal, liberal arts environment. Wonderful alumni network. Small classes, probably taught by professors.
At Williams, a wonderful music department by reputation The site says 500 students participate in music and there are "approximately 125 concerts a season ranging from student recitals and ensembles to visiting artists of national and international stature. " Students can play in the Berkshire Symphony. There are lessons, chamber music, and advanced music performance classes for credit.
Princeton is in an affluent suburb, close to NYC by train, very different location. The larger undergrad body is broken down into smaller communities in the residential system. http://www.princeton.edu/main/campuslife/housingdining/undergraduate/
In our experience with another Ivy, this house system is extremely effective in providing the intimacy of a small school within the walls of a larger university. Students develop a real feeling of home, hang out in the dining hall, and have adults around consistently for support. However, the presence of the larger university and many other houses means meeting that many more people in your department, in your activities, and less claustrophobia for some who prefer access to more social opportunities.
Princeton also has a performance certificate http://www.princeton.edu/music/certificate-of-music/ and by offering that, honors the needs of musicians who want to have access to opportunities in “applied music”, aka performance. This means lessons and performance opportunities for credit and some classes with a performance component. There is also a double degree program with the Royal College of Music in London.
Finally, a drawback to universities can be the system of lectures with grad students teaching sections, and grading, so that students do not develop as many personal relationships with faculty. and learning might be more passive, so to speak. However, liberal arts colleges will indeed have some large lecture classes, including sciences, and at the same time, the music dept. at Princeton will be a relatively small department with more interaction with faculty and smaller classes.
Princeton has grad programs in music for composition and musicology. I don’t know if undergrad musicians get to play grad student compositions, but I do know that Princeton has a top notch, progressive, very creative composition PhD program for composers and wonder if that could be an asset. I don’t know but worth asking.
I think these two are both wonderful options. In some ways… I would lean toward Princeton if the musical experience can be personalized, if the house system offers community, and your son finds the the larger university and relative proximity to NYC appealing. But then again, Williams offers an assuredly personalized experience in beautiful surroundings that aren’t that far from NYC or Boston, and has a vibrant music department. Tough call!
It may just come down to your son’s personality and gut feeling after visiting!! Let us know!!