My family is like your opposite – live close to Princeton, though my wife grew up near Stanford and all her family still lives very near it (walked the campus too many times to remember). So we’re more familiar with Princeton but fairly familiar with Stanford (my wife’s brother and her father also went there).
You can’t go wrong either way of course. I do know the music program at Princeton decently well – my HS son did some DE courses there in music performance (jazz). He loved it. They have a large music faculty and also supplement it with accomplished visiting faculty. The classes were small, particularly the music performance ones, and not too hard to get into, even for our HS student who was below freshman in the pecking order. Princeton U has a great, architecturally interesting building dedicated to music and many incredible places to perform in. I would recommend it. Our son told us he had heard Stanford was playing catch-up on building up their music department, but was actively bringing on some great faculty.
It’s interesting you say the rep is that Princeton is more competitive and less collaborative. Everyone around here has exactly the opposite impression – that Stanford is the more “sweaty” competitive of the two. No idea if rep either is true, or if both are. I know and my kids have known many people who went to PU and they all are/werr happy, without exception. My daughter had a close friend go to Stanford who had been one of those effortless tippy top students in HS and ended up so stressed at Stanford she took a year off before resuming with a changed major. Not implying that experience is the norm.
I have heard elsewhere that Princeton’s grading has gotten less intense recently but don’t have imperial evidence of that. This article says the average PU GPA is 3.49 which seems decent and it’s very close to half of the other Ivys.
Princeton is a great college town. Both campuses are beautiful.
Good luck with your win-win decision.