University Honors requires students to live in Lechner/Mosher/ and one other dorm I can't remember. I highly recommend freshman live in an honors group. It significantly reduces the chance of being paired with a roommate that parties his way to academic probation his first semester. Also easy to form groups for homework and studying. Being surrounded by geniuses is good for future networking and also refining any studying deficiencies that may have been acceptable in high school, but need to improve for college. I'd recommend it if your kid isn't 100% sure he wants to do engineering.
You can do both, so start out with both if he has the opportunity.
Make sure engineering honors allows you to register for classes early or provides guaranteed access to smaller classes with better professors. Honors used to "basically" guarantee that your professor was a native English speaker (can be a huge benefit) and there were 40 kids in class instead of 300. Both programs allow your kid to take honors classes. This is the second biggest benefit after early registration, and very important for the first 2 years.
I believe it's correct that Engineering honors is only in Dunn, HOWEVER those are kids that are engineering honors only, and not university honors. The university honors kids overlap a lot, and they live in Mosher/Lechner. There might even be more of them there than in Dunn.
As far as which to live, Mosher/Lechner is going to be the more nerdy place. If your kid's friends are in math team/band/orchestra, that's the place for him. If your kid's best friends are in athletics, live in Dunn. He will fit in better there.
Not a popular opinion, but I don't think university or engineering honors matters after the first 2 years unless you're applying for prestigious law or medical schools. Upperclassmen can usually get the classes they want, classes are already smaller, and research is more valued in academia than industry. Engineering employers rank by GPA and internships more than research conducted with a professor.
Disclaimer - my experiences are from decades ago, so discount anything I have said if someone with more recent experience disagrees.