If you google something like “[college name] financial statements”, you can usually find a financial statement that contains information like their operating budget and operating revenues.
A few things to note.
This doesn’t include capital expenditures, which of course is a significant part of the value (the buildings and facilities and such).
When a institution has a medical center, it can be tricky–you just want to make sure you are not including revenues that are spent on medical services, just net revenues that are free for other institutional expenses.
Finally, if an institution has graduate and professional students, ideally you would break them out separately, but usually this is not possible.
But still, you can at least get a comparative idea between generally similar sorts of institutions. And yes, the wealthiest institutions tend to spend far more in just operating costs per student (which again doesn’t even account for campuses and such) than they charge even for full pay, and that is at least one potential reason to actually see them as more valuable.
But my two cents is like most things, this is probably subject to a diminishing marginal utility. Meaning if College A is spending $X/student to provide a solid education, College B spending $2X might add some value, but probably not twice as much.
But this IS a very common issue. Like, if Family A spends $Y to get a modest but comfortable family home, then Family B spending $2Y in the same market might get some more value, but probably not twice as much. And so on.
So, if you are the sort of family who would be full pay to begin with, you are likely facing these sorts of choices all over–you have all the basics covered, you still have financial means left over, and basically any way you spend it (holding aside giving it to a small charity, perhaps, where the marginal utility might be pretty high actually) will have diminished marginal utility.
Which is fine, at that point you just pick whatever you like best. And if that is spending more on college, that is not necessarily worse than other ways you could spend that money.