It likely depends upon where you live. If you live in the northeast/New England world of the old line WASP, prep, yacht clubs, Wall Street, Hamptons, country clubs etc then hands down Dartmouth will have the superior reputation and if you live in the south it’s probably Duke. Out west it’s probably split but others can opine. I am certain though that academically there is zero difference. It’s more a matter of what social aura you are comfortable with. Duke, Chicago, Wash U (all equivalent in my view) are world class universities and ranked higher than some Ivies, but Dartmouth certainly has a significantly higher “it” factor in in the Northeast and will grant you access to many more “places” if you care about those things. Summary = equal Academically but very different Culturally.