I recommend you visit the AA/UA fora. A little bit of searching and some time spent reading the stickies will give you a lot of insight into both airlines.

One of the AAdvantages (pun intended) of AA is their undocumented elite status "challenges". You and your wife can earn gold or platinum status with just one trip to Europe. Then you start earning bonus miles with your flights and have access to first class check-in. There's a sticky at the top of the AA forum that explains this in detail.