ease of using the award booking program (e.g., ability to book partner airlines online)
You won't find this on AA. They do not have any way to search for partner awards via the AA site. You'd need to use some other sites (BA/QA/JAL) to see if you can find a partner award and then you'd call in to AA to get it booked. If this is a very high priority for you then you will be a bit disappointed in AA.
If you hadn't listed that desire to book partner awards online, I'd definitely recommend AA. Although, my impression (and this is not based on any facts other than general impressions from reading FT) is that UA/CO has more options on semi-direct routings to Europe. Many AA end locations will end up with a flight to MAD or LHR and then a IB or BA connection on to your end point. I just have a feeling that UA is a bit better about minimizing connections in Europe. Definitely read up on the UA forums to judge for yourself though.