I was Exec Premiere with United a few years ago, and I have been Platinum for three years with AA. In the last 10 years, these two airlines have accounted for about 75% of my domestic flights, with numerous upgrades on both.
In all, I've both good experiences and bad on each airline. But almost without exception, the quality of service and general comfort level I have experienced on most foreign carriers (especially Qantas, but also British Air and South African) has been better than the international flights on either AA or UA. Unfortunately, a trend I have noticed with both airlines is that the general level of service (domestic and int'l) has declined during the last few years -- in part because the planes are so full these days.
But if I were to try and compare apples to apples between AA and UA only, the biggest difference is that UA seems to treat its elite members and business/first flyers with a tad more respect and restraint than AA. The front cabins feel professional on UA, whereas they are sometimes a bit too casual on AA. On the other hand, UA also seems to actively DISrespect its non-elite flyers -- something I don't find with AA.
Since losing my Premiere status, the recent times I have flown UA have rarely been pleasant. A lot of UA employees don't seem to care for their jobs, and their dissatisfaction seems to be taken out on the average flyer. At best I feel like just another member of the cattle call -- at worst, frowned upon. Prior to gaining elite status with AA, I never felt like I was treated special, but I generally had positive, upbeat interactions with all manner of staff.
In then end, I'm sticking with AA over UA in large part because of their frequent flier program (which I feel is more generous, particularly with partner awards) and also because their route network serves me a little better. But if those two items were equal, I'd still lean to AA because I'd prefer to have upbeat, smiling, if sometimes lax interactions with an airline's employees over formal, play-by-the-rules, if usually professional service at another airline.