I even earned a masters degree from a Big 10 university. The big rivalry in that region was always Michigan/tOSU, and it was often billed as a clash between two superpowers, like the USA vs. the Soviets during the Cold War.
While living in the Midwest, I was asked to describe the rivalry between BYU and Utah. Rather than compare them to superpowers clashing, I described the rivalry as being more like the Israeli/Palestinian conflict, where you have two sides that live amongst each other, and the conflict runs much deeper and more personal than a geographical allegiance. The Holy War name fits this comparison.