By the same metric Duke loses to Cal Poly…
The cross-admit comparison is more or less a pointless metric, except when it does come in handy curing some insecurities (if it doesn’t backfire). Manipulating yield is no more than a part of a school’s admissions game these days. I don’t think Cal Poly is really a better school, nor do I believe any of these people chose Cal Poly because they think Cal Poly is better, but it proves certain points.
Duke is a great school but I would choose Columbia, Penn, Dartmouth and Brown over Duke anytime, not because they’re Ivies. I don’t think any of these schools is substantially better than the others. At the end of the day, it all comes down to personal preference and maybe how much money these schools are offering.