This is something no-one seems to have pointed out, but, if you fly mostly PAID business class, AA allows to reach PLT faster than UA (with points). In other words, you earn 1.25 point per mile flown, and only need 40,000 paid BC miles to make AA PLT (equivalent to 50000 points). Depending on where in Europe you fly, AA's European route network is slightly better than UA (Madrid and Stockholm come to mind). If you fly to other cities that don't have translatlantic connections, connecting in LHR to BA (or any other 1world partner) will get you elite bonus miles on all your flights, something that unfortunately is unavailable on the * Alliance (except for transatlantic LH flights). Then there is the fact that on AA you can use miles to upgrade international flights on any fare (in case you ever have to fly econ).

On the other hand, UA has a better route network to Asia and over the Western US in general.