Chicago’s economics is not superior, it is superior if you want to study and learn neoclassical economics (monetarist and fresh water economics type). Columbia’s economic department is a saltwater one and has its huge share of New Keynesian economist. Both are considered mainstream economics department and will be teaching those outdated basic intro neoclassical theories from the textbook for UG. So, there is really no difference since you will get the grounding in marginalism and general equilibrium models. The RBC, NK, and DSGE models is the core of mainstream economics which all focus on general equilibrium, you do not have to worry about this unless you go on to graduate school in economics. However, I would assume at the UG level, the department will at least have a bit of those preaching of Freshwater vs Saltwater ideologies.
Neoclassical vs Heterodox Economics and which program that gives you those perspectives.
1.Neoclassical (Mainstream Traditions)
Freshwater Schools (Monetarist, Rational Expectations, Supply Side Economics) - Chicago, Wisconsin - Madison, Minnesota, U Mich, Rochester
Saltwater Schools (Neo Keynesians and New Keynesians) - Columbia, Yale, Harvard, Berkeley, MIT, Stanford, NYU
- Heterodox Traditions
Left Heterodox (Post Keynesians, Marxian, Feminist Economics, Ecological Economics, Institutionalist) - U Mass Amherst, U Missouri - Kansas City, The New School, Colorado State University, University of Utah
Right Heteroodox (Austrian Economics/libertarianism type) - George Mason U, Florida State U, Auburn U, NYU (used to have some big name austrian economist there for their phd program faculty and teaches austrian economic at graduate and ug level)
- Some reading before you take nonsense advice from people about any university's economics department. Learn some of their history and what they are teaching.
http://noahpinionblog.blogspot.com/2011/04/what-i-learned-in-econ-grad-school.html
http://www.nakedcapitalism.com/2011/09/economics-debunked-chapter-two-for-sixth-graders.html
http://www.slideshare.net/UmkcEconomists/2014-introduction-to-heterodox-and-post-keynesian-economics
Most if not all PhD student or professors in economics use these two literature to compare program rankings. If you are a neoclassical you would use grijalva-nowells ranking if you are heterodox type you would use fred lee:
http://ricardo.ecn.wfu.edu/~cottrell/OPE/archive/0409/att-0052/01-Heterodox_GRADUATE_PROGRAMS.doc
https://openeconomicsnd.files.■■■■■■■■■■■■■/2009/06/grijalva-nowell.pdf