I'm certainly not loyal to either, but in very general terms I've found UA's domestic route network out of ORD to be preferable to AA. There are several mid-size cities where UA offers at least some mainline service while AA has only Eagle service or no service whatsoever (eg ALB, BUF, SMF). UA offers nonstops to ANC & HNL -- AA doesn't.

Of course, as others have mentioned, AA might be better depending on your particular destination. AA offers the only daytime flight to LHR which I prefer to the overnights.