That’s an excellent question.
On the one hand, there are some programs within lesser schools that are excellent and noteworthy ( both for scholarships and job opportunities).
On the other hand, how many people do you know who work in the same field as their major?
I have gone to both interesting/good schools that match a specific job and highly ranked schools which open doors. When studying, the specialized programs tend to be very good and you might find like-minded individuals. They might also be cheaper.
On the other hand, no one ever hired me based on those programs once I got the big named brand U as well. People love the big name U. It lessens the risk for the hiring manager.
I would ask the student, what is the likelihood of going into various specific majors? What is your budget? What type of work do you want to do long term? If you just want a normal job, then great go anywhere. IF you think you want to work in management consulting, then go to Name U.
Another HUGE consideration is the amount of money you will make. In my 20’s and 30’s I often made 2-4 times more than others my age who had gone to normal schools. Why? The name of the school. This decreased after about 20 years but it was still considerable, allowing me to buy a house and start businesses. Over time this leads you into a different place. Over a lifetime you could be talking several million dollars or getting financing for your company or not.
I’d advise my own kids based on how clear their plan is, what the likelihood of them doing and being successful in different jobs looks like and relative reputation of the school. Also, if it’s just a good school, then I’d advise it’s a large school so there are more alumni. I’d advise them not to attend a school that’s great in only 1 area.