In the scenario where it was no debt vs. a hundred Gs, I would choose the "elite" only if it was between an elite school and an absolute dud of a school (i.e., I wouldn't go to one of the fourth tier schools just to avoid paying, you'd just be astounded by the folks around you). If it was between an elite school and a "good" school, there will always be resources at a good school for an elite student to challenge themselves if they want to.
The only exception to that would be if I was dead set on doing something like managing a hedge fund, where it seems like every single name on the prospectus has a ph D from an elite school or some other post graduate ivy league degree.
Or if you wanted to work at a multinational law firm, but why anyone would want to do that for more than a year or two is beyond me.