The quick study says the UA CVG-ORD-BHM flights are about 4.5 hours travel time. DL CVG-ATL-BHM clock in at 3.25 (for the 2 early am flights) but mostly about 3.5 to 4.0 of travel time....
I might give you a different answer if there was direct BHM... but since you are connecting anyway, I'd personally stick with UA.
Side note, I was usually (80%+) upgraded ORD-CVG (and v.v.) as a UA Gold, and 100% as a 1K