Pick UChicago if ultimate career goal is prof., PH.D, etc

UChicago is very much learning for learning's sake.
Focus: knowledge discovery & development
Nickname: where fun dies
The mandatory core requirements include reading a lot of classics, which prepares well for a research & academic career.

Duke: quite balanced on academics & student life.
Sports crazy. School is very much bubbled (i.e., you do everything on campus, much like Stanford), while UChicago is an integral part of a big city (much like Columbia & UPenn).

Some students like a bubbled campus life, some don't - up to personal taste

For a business career, both schools offer plenty of opportunities. Duke may slightly have an edge for undergraduate, while UChicago is a tad better on graduate programs, but the differences on reputation is small enough.