I went to a major state research university for engineering. During career fairs, the big companies would always have huge lines for hours and the unknown, smaller companies would be doing their best to grab every uninterested kid walking past. The big companies were usually a waste of time to talk to (and waste of time waiting to talk to). They would sort resumes by GPA and pitch the bottom 90%. Then you would still be competing against everyone at every other school in the region. Unless you are just looking to name drop your previous employers, the experience is really what matters. I would usually go right to the smaller companies and be able to have actual discussions with an engineering manager or even a VP. Those companies would almost always call you back and be interested for an actual interview.