Advice for my brother who's planning to apply early to one of them.
US News has Penn and Chicago tied at no. 5 nationally along with Stanford, MIT and Caltech. Columbia is ranked slightly higher at no. 4.
For econ definitely wharton for undergrad. I have met a few chicago undergrads and It seems like there is a high variance in terms of their wrote knowledge. Also my public school was noted for sending students to relatively good schools and it seems that the kids who went to Chicago could not get an admit to any Ivy.
I agree with you- the rigor of a Chicago undergrad education is well-known in academic circles.
However, Wharton has much stronger Wall Street recruiting. If you get an average GPA at Wharton UG, you'll likely get into a bulge bracket investment banking analyst program. Only Harvard has similar recruitment opportunities.
Cross-admits would surely pick Wharton over Chicago and likely pick Penn A&S over Chicago. This might be changing, as Chicago is closing the selectivity gap.
The exception to the above are high performing math and physics students, who would likely choose Chicago.
Wharton is not better than Chicago. Wharton is like doing your MBA for undergrad. Chicago undergrad is like *real* grad school.
When I did my doctorate at Chicago and loved it. But the undergraduates there were ... weird. It seemed that they could not wait to be in grad school. (They are not Frosh, Soph, ... but 1st year, 2nd year in the 'college.') I applaud ambition and all but the administrators kept trying to find ways for them to have fun too. The unofficial motto was "Study Naked" - those crazy geeks.