Both great research institutions, but quite different.
I did my MBA at Chicago, undergrad at NU. My wife, a UC undergrad, teases me about attending college at a "finishing school" but readily admits she would drive up to NU to party.
I loved mt time at NU, but what is amazing about Chicago is the intellectual power. The business school basically built the foundation of modern finance theory. Stiller, Friedman, Merton Miller, Gene Fama, Fischer Black, and Myron Scholes are some of the most known names in finance who did their research at UC.
But what is truly revealing is the rise of behavioral economics at UC. The same institution that gave us free markets and rational investor theory also gave us the theory on why humans make bad or irrational decisions (turns out not necessarily irrational, just unknown assumptions about what we value). Two diametrically opposed ideas coming out of the same school. That amazes me about UC.