UChicago has 978 milliHarvards (mH) of prestigiosity, Cornell has 980 mH, and Cal is at only 900 mH. (Source: http://talk.collegeconfidential.com/parents-forum/1457519-is-it-time-to-revise-the-prestigiosity-ratings-the-original.html)
I think the clear choice is Cornell; if you attend UChicago, and have to compete for a job with a Cornell grad, a prospective employer will consult their prestigiosity table and throw away your application right away.