Really, you have no dilemma at all, at least none concerning the University of Chicago. If you want to be an engineer, then you want to go somewhere with a good engineering school. That includes Duke, Penn, and Cornell, certainly, and does not include the University of Chicago. Duke, Penn, and Cornell also have first-rate departments across myriad disciplines, so you will have plenty of choices if you decide to change majors (and, everywhere, it is fairly easy to shift out of an engineering program, but difficult to shift into one midway through college).
Chicago is a great university. Personally, I believe it offers a better undergraduate education in most fields than Duke, Penn, or Cornell (which are nothing to sneer at, by the way). But not engineering. If you want to be an engineer in any kind of traditional way, that means that you don’t want to go to the University of Chicago. It’s that easy.
If there are things you like about Chicago, you can find equivalent courses or programs at the other colleges.