There is no evidence that the teaching at the most prestigious schools is better, so two remaining reasons to send one's children to them are to get a more valuable credential and to mingle with smart, well-connected students.
There's another consideration: standards and expectations.
I went to college in western Massachusetts. There are 4 colleges in that area, plus one big university (UMASS). The college I attended had very high standards, almost across the board (this was in the 1980s). The standards were also very high at the other two small colleges where I took courses and had friends. I would not say that the same was true of UMASS at the undergraduate level, at least in the departments I studied in and the ones I knew a bit about, except for Physics. I don't know about other science departments.
The professors at UMASS used a lot of multiple choice tests. A good friend there got As on papers that would have got Cs or less at my college. I remember studying for an Archaeology final on the bus on the way to the test. I got an A --- not because I'm so smart, but because the class was so easy. It was all memorize and regurgitate. My college had very few classes using that format. Even the "easy" courses required lots of writing and short/essay-answer tests.
All the small colleges in that area are undergraduate-focused, which may improve the overall quality of teaching.
That said, I don't know what things are like now. Grade inflation trends may have changed things.
Out here in CA, I've taught at a local community college. Again, the standards are nowhere near what they were at my alma mater. Lot of multiple choice tests, and even rules about grading. For example, I taught a short courses at times. In these courses, I wasn't allowed to give out a C- or a D+ (A- or B- was okay). The system wouldn't let me enter these grades and the choices were C or D. I suspect that this policy was there to ensure that you didn't hand out too many grades below 2.0.
ETA: a friend also attended a small liberal arts college, but this one was not in the top tier. The standards at her college were also low.
