I agree with @eyemgh. Other things to consider - job placement, not just post graduation but for internships and co-ops. Reach out to the career centers of the schools on your list. See how many companies come to campus, % of students who get placed, etc…
I also don’t think you can discount a school’s willingness to accept AP and DE credits.
Remember too that the big state schools have honors programs that have their own classes and profs.
I forgot, one of the most important things we paid attention to, happiness. Schools with reputations as grinds, or where students were competitive rather than collaborative, were eliminated. My son is a Mechanical Engineer. With over 300 programs to choose from, neither of us felt it was worth choosing a program where the suicide rate was far higher than average.
The school he landed at actually has pretty significant grade deflation. Students have a “we’re in this togetger” mentality though. That probably because even with an average graduating GPA of around 2.7, close to 100% are employed in engineering jobs or at graduate school by 6 months post-graduation. Pretty impressive for one of the largest ME departments in the nation (just over 1200 students).
You don’t need ABET for Computer Engineering, and it would only be helpful if you were on the power distribution side of EE, and my degree is EECS.
You don’t need ABET for Computer Science. But for Engineering, I would definitely pick a school which at least receives ABET accreditation for the program I am interested in. Yes, the number of faculty members does not affect undergrad teaching quality. In fact, those top faculty members most likely do not teach undergrad courses. But the research facility and the range of research conducted will be affected by the number of faculty members in the program. You tend to see close to 100 or even more faculty members in any specific engineering program at top engineering schools.
“You don’t need ABET for Computer Engineering.”
This is not the place for debates about ABET, but do not take this to mean all non-ABET accredited programs are good. A reasonable rule of thumb is that nearly every good program is ABET accredited and nearly every non-ABET accredited program is suspect. There are exceptions, but they are few and far between. They are widely recognized names in engineering, Stanford, for example.
https://engineering.dartmouth.edu/academics/courses/undergraduate lists Dartmouth engineering courses. The five year issue is another drawback beyond the limited offerings. (The heavy fraternity/sorority presence may also be an issue for the OP.)
Of schools comparable in prestige that some (not all) take as the measure of quality, Dartmouth seems to be more limited in engineering than most others. So if the OP prefers prestige over UIUC (or wants to avoid specific drawbacks of UIUC like the difficulty changing major), there are likely many other schools that offer that but are not as limited in engineering.
I think you’re putting the cart before the horse 
If you’re in the application stage, then Dartmouth has a 95% rejection rate. Right now, it’s not even a debate unless you have an acceptance letter from both schools. Relax and just go with it Be sure to apply to some safety schools. I would also apply to scholarships too.
Historically, engineering was viewed as a lesser pursuit (academically speaking) compared to the harder sciences or humanities. It was sort of viewed as the practical topic that lower and middle class students studied at university while the wealthy and well-connected could study more classical, high-minded things. During this time period, Ivy League schools (and other similar schools) largely ignored engineering as being beneath them and it wasn’t until (relatively) recently that any of the Ivies actually cared about engineering. Meanwhile, most of the land-grant universities were established around, among other things, engineering programs, and have been doing engineering for literally their entire existences. This is the historical reason why many land-grant institutions are “ahead of” most of the Ivies in engineering.
That being said, there is a kernel of truth to the idea that the fundamental ideas of engineering are pretty standard and that a student will get the same basic fundamentals at any reputable program (for example, any ABET program and the few non-ABET programs that aren’t trash). However, you can’t sit there and argue that a program is better because it has better students while also arguing that all programs are effectively the same because the basic fundamentals of engineering are fairly standardized. If nothing revolutionary is going on at the “top” schools, then how is the reverse true at Ivies? The fact here is that engineering is much more egalitarian than other fields.
So, let’s back to one of the original questions about what concretely causes most of the Ivies to be perceived as inferior in engineering to their land-grant brethren. The Ivies started late in the field, as I mentioned before, and haven’t devoted many resources until (in some cases) relatively recently. The programs were therefore small and underdeveloped for a long time while state schools built up a reputation in engineering. That means that now, it is actually harder for most Ivies to attract the top faculty in engineering (with some obvious exceptions), which has an affect on the programs. As an engineering professor, Princeton and Cornell are literally the only two Ivies I would even consider as a place to work without some pretty substantial changes. Otherwise, they simply couldn’t support my research program (or maybe just won’t).
Now, all that being said, that doesn’t mean a student would get a bad education in engineering at the Ivies. The curriculum is somewhat standard, after all, and a number of Ivies have been putting more resources into their engineering programs and trying to attract more top faculty, especially in newer fields like the biomedical sciences (which is getting a lot of investment at Harvard, for example).
One more note, since it was discussed earlier, is that department size can be correlated positively with program quality. A larger department means more professors, and more professors means more diverse interests. This means the number and variety of electives is going to tend to be larger at larger programs. Now, of course, I used the word correlation for a reason, because it’s an indirect relationship. You could certainly have 100 faculty at a department and they are all doing the same research or just not doing research, at which point it is unlikely to contribute to a breadth of research and elective opportunities. At the other end of the spectrum, you could cite some of the really “elite” schools that have excellent reputation despite small size. Still, my main point is that you shouldn’t discount a school simply because it is large. That can have some advantages.