Can only speak anecdotally. D had two HC friends in engineering. Both chem. One did internship and REU and is now in PhD program in geology. Another did a summer abroad, internship and had a job lined up before Christmas for this summer after graduation. Honors gives you opportunities to make good connections and they encourage research with professors. Magellan grants will pay you to do research (D had one in math) and I assume that makes it easier to get in with professor when you can bring some funding of your own. HC gives you an honors advisor for your major which gives you another level of help in figuring out classes. Smaller classes and professors (as opposed to TAs) for even entry level classes. Great fellowships and scholarships office to help with those kind of opportunities (NSF etc)
I’m sure if you call the HC they have someone who can give you more information about where students have gone and more hard numbers on how graduates do. They could also refer you to a contact in engineering. I think most programs have a professor that coordinates HC courses for their majors.
I can’t say that USC is stronger or as strong as UMD or NC State, but if you take advantage of all the opportunities offered, then as a individual, not a statistic, you can do amazing things at any school. Good luck.