My 2 cents on this:
Both Chicago and Wharton are equally great schools in terms of academics and reputation. Wharton may have an edge in terms of reputation in Asia but in the US and Europe, i believe both Chicago and Wharton are at par.
Having visited both schools, the differences i could "Sense" are:
1. Wharton, despite a larger class size has a closer knit student community than Chicago because of the fact that most students live in the same area
2. Chicago seemed more polished and friendlier than Wharton
3. Chicago students seemed to take more pride in their school than Wharton students
4. Chicago administration is doing a better job at keeping the alumni and students together and engaged with the school. reflected in broken emails and contact details of alumni at Wharton. nothing of that sort with Chicago
5. In terms of faculty, Chicago seems to have almost as good if not better, a faulty as Wharton
If i were fortunate enough to choose, it would be a very tough choice and probably scholarship if any, could play a major role in my choice.