I have been asked goodness knows how often whether Yale is "better" than Princeton, or whether Harvard is "better" than "Yale". My standard and truthful answer is they are all really very good and that your kids will get the same quality education at any of those places.
Indeed, you kids will be so so very lucky to be able to get into any of these and many other high quality universities.
Getting into a branded college will be increasingly difficult as real income rises around the world. Families with high incomes would want their kids attend a "famous" university. Hence, demand for a Branded Name college would greatly outstrip supply.
The entire student body including graduate students at Princeton, for instance, is just a bit above 7000. At Harvard, about 20,000. These are small numbers considering students from all over the world all want to attend one of these schools. If you net out graduate students pursuing a Masters, PhD or a professional degree such as an MBA, the college student body size drops further. This means "supply capacity" of universities is quite limited.
Right now admissions rate at the top universities is in the high single digit. That means for every 100 applicants, mostly already self-selected as qualified, fewer than 10 get in.
Before long, say in less than 20 years, that digit will be a low single digit. I suspect in not more than 50 years, the admissions rate would drop to below 1%.
The question still remains to the privileged few who must choose between or among several colleges who have admitted them. How should they choose.
My first cut is to look at the ranking of endowment per students. This applies to junior and senior high schools as well. Before I show you the ranking, I must also say that the rankings do NOT suggest you cannot get an equally good perhaps even better education at publicly funded schools or universities.
What the rankings suggest is that you are likely to get more TLC in hardware -- by way of quality and quantity of facilities -- and "software" - by way of individual attention, faculty access -- at those schools per dollar you spend on yourself. In other words, all other things being equal, you will be better pampered at a school with a higher endowment per student than at a school without that kind of money backing you up.
The list for colleges is here. Data are somewhat outdated, but I suspect the ranking has not changed that much in the past 4 years.
Here is the list for 9-12 graders.
In both lists some religious names are among the top. For those with a particular religious focus, these lists can be helpful.