Actually, if the measure of admissions difficulty is how many people are accepted in comparison to the number of applications, then both schools are approximately the same.
armcp - your argument has nothing to do with this acceptance rate; rather you attempt to compare the quality of the applicant pool based on two numerical parameters...scores and rank....and then you attempt to extrapolate a 'level of difficulty' from those parameters. Tricky business that is.
Btw....you should know, Duke does also give weight to your so-called "soft factors" as well. In fact, the legacy, URM, hook factors go a lot further at a private institution like Duke than a public institution such as UNC...so your last statement doesn't even make sense to me (and I have worked in college admissions).
(Btw...this is such a h.s. senior topic. By sophomore year of college, most people are over it.
)