Unless I am mistaken, at Illinois in order to major in two subjects in two different colleges (Physics is in Grainger, Philosophy in LAS), you have to do a Dual Degree, not just a Dual Major, with admissions granted by both colleges. I’d check carefully into exactly what that would mean for your daughter, including how many other sorts of things she would be free to explore outside those programs after satisfying all their degree requirements.
WUSTL makes it way easier to do dual majors, including between colleges–although for them Physics and Philosophy are both in Arts & Sciences. So I believe the way they do it would leave open a lot more credits for other things too. But you could map that out and see.
I note WUSTL also has a Philosophy of Science major that is specifically designed to be a second major combined with a primary major in a science:
https://bulletin.wustl.edu/undergrad/artsci/philosophy/#philosophy-science-track
I am not sure what your daughter is interested in when it comes to Philosophy, but I personally think that is very cool (full disclosure–I was a Physics major who switched to Philosophy but stayed interested in the Philosophy of Science and Philosophy of Physics).
In terms of grad school, I note Illinois had over twice as many PhD placements in a five-year window as WUSTL in this study (1555 to 732):
However, Illinois has nearly 5 times as many undergrads (about 35000 to 7500). If you do the math, WUSTL undergrads were going on to PhD programs at around 2.2X the rate of Illinois undergrads.
That doesn’t mean you can’t go to great grad programs out of Illinois, but I think it may help some WUSTL students that it has a much lower student to faculty ratio, and likely more opportunities for students to build the relationships with professors that can help them get placed in top grad programs.
That being said, in Physics specifically, Illinois has a great department. I think WUSTL has a very good department, but not really on Illinois’s level. I think that really matters most for grad school, but if your daughter was completely focused on just Physics and really liked Illinois’s department, that could point in their direction.
But given your description, and also the large possibility of actually changing her interests in college, I would think carefully before putting too much weight on that one department.