I think ND has more cache with a lot of companies in the Midwest and East than Stanford does. I was pretty reasonable with my analysis. It depends on who you're talking to and why. Stanford is the King of California but a lot of people in the Midwest don't know much about it if they've even heard of it. They have an outstanding faculty which means their academic cache is almost unassailable, and their engineering and connection to Silicon Valley are also amazing. But when it comes to employment opportunities and salary, ND engineers do just fine relative to their Stanford counterparts.
Anecdotally, I went to the best high school in Ohio (by average SAT). Our class sent people to Harvard, Johns Hopkins, ND, Chicago, WUSTL, UCLA, Cal, Dartmouth, Annapolis, and West Point, among others. As far as I know, no one even bothered to apply to Stanford. That might be changing with their athletic success (Flutie effect) but for now Stanford is mostly California in a 'universally known' sense and national in an 'academic and top tier industry' sense. For that to change, I think they'll have to start accepting more than just a few people from each state outside California. Last I saw, they had something like 800 enrollees from California and only a few dozen from the next highest contributing state.