<p>I've heard that prestige of the university is not so important when it comes to REUs ... but, what then, distinguishes a more "top-choice" REU from a less favorable one?</p>
<p>From what I have read, a lot of people end up applying many REUs they are interested in and praying to get into at least one, regardless of the university name/rank. </p>
<p>Also, at the time of graduate school admission, are all REUs respected equally? </p>
<p>The success/prestige/respect/etc. of an REU isn’t based on which program you go into as much as what kind of results you get out of it. And while this does depend somewhat on how bright you are/hard you work, a lot of it also has to do with being provided accessible problems where tangible results are possible. So I would say that the ‘top-choice’ REUs are the ones with a history of providing these kinds of problems to students. You’ll find that a lot of them are in discrete math, where it’s not too hard to put twists on previously known results that are tractable, yet haven’t been considered yet.</p>