I don’t understand what is meant by “intellectual diversity”. Does it refer to abilities (average-smart-brilliant)? Does a class mostly populated by brilliant students create an Ivory Tower environment that is less than ideal w.r.t. to some learning objectives? If that’s the claim, how would we test it?
Does it refer to diversity of opinions? Of interests? Of academic programs? Many “elite” private universities (and nearly all LACs) have a strong focus on the liberal arts. They deliberately exclude pre-professional training in agriculture, architecture, nursing, and sometimes in business and engineering. So they’ll have an advantage in outcome metrics focused on achievement in the arts & sciences over large schools that cover many of those pre-professional fields.
If Ivy League colleges are elitist, narrowly focused Ivory Towers, then for better or worse, “Ivy equivalents” share similar characteristics (including high concentrations of high-stats students). If you think another kind of college has desirable characteristics, then identify another set of indicators that they out-perform. Then rank according to those indicators. Like this:
http://www.washingtonmonthly.com/college_guide/rankings-2015/national-universities-rank.php
(UCSD #1, Michigan #13, Duke #31, Yale #44, Chicago #55, Dartmouth $64. )
If you think this ranking better reflects your interests, needs, or values, then you have a basis to confidently choose Texas-El Paso over Rice, Vanderbilt, or Duke. You shouldn’t care too much about identifying “Ivy equivalents”.