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Career Fairs are just a sample of companies that recruit at any given schools. Lot of companies will have individualized info sessions at these schools to advertise jobs during accessible evening hours rather than set up a small booth at a Career Fair that most students will miss since they have classes to attend during the day.
Objective data shows that its easier to get access to research opportunities at Columbia and Duke over Illinois or Michigan since they have comparatively smaller engineering programs so its easier to get access to faculty and receive more individualized attention.
However, its not accurate that Engineering doctoral programs will prefer a Michigan engineer over a Duke engineer or an Illinois engineer over a Columbia engineer just because these state schools have stronger graduate programs in these fields. It will come down to the performance of the individual student and the research opportunities that the budding engineer has had while at school.
For example, the quality of teaching and research standard of Berkeley Civil Engineering is the best in the world. And, Berkeley's mechanical engineering is slightly superior to Stanford's and Caltech's.