UofC is ranked much higher than Yale for Sociology, although Yale of course has a much higher general "prestige" factor, particularly among those who aren't in academia, because it is an Ivy. I have also heard that UofC can be cutthroat, because the department basically structures the program in a way that grad students have to compete for funding. Academic placements among Yale PhDs have been notably less impressive than UofC.
I would say if you were really concerned about getting an academic job after receiving your PhD, go to UofC. If you are more risk-averse and would consider jobs outside of academia, go to Yale.