Main reason the AA 763 two-class planes are nicer then the UA two-class 763s and 772s is that AA does not have a three-class 763 anymore, so they had to offer a fancier Business Class for international runs since they no longer offer First except for the 772s. For UA, a two class 763 or 772 is just a way to funnel a lot of leisure folks between two destinations, with a large First Class cabin for both upgrades and the surprisingly decent paid and award bookings.

So when flying top-level international on a 763, advantage UA thanks to the wider First seats and extra benefits of a true First Class cabin.

Of course, when flying two-class domestic, AAdvantage AA.