The relationship was almost surely closer with BA - they took over routes using wet-leased US planes. AA at the time was little more than a code-share partner. Of course, both relationships basically ceased when AA & BA joined in OW.
Personally, I have no doubt that US needs an alliance more than an alliance needs US. The same goes for a merger with a major carrier. However, opinions vary as to which alliance is the most desirable - *A claims the number of carriers/destinations, OW claims the "class" carriers, and ST claims something I'm sure. Whose claims ring most true probably depends on the traveler as much or more than the alliance.
Jim