Depends on your paid class of travel.

If buying first or business class tickets, make UA your main LAX airline and use the bmi loyalty program, not Mileage Plus. This is what I do because I travel mostly long-haul premium cabins. For the fewer UA domestic flights, I either buy Y-UP fares or do paid upgrades-for-cash at check-in --- the good thing is that UA sells these upgrades before upgrading elites on day of departure.

If flying on economy tickets, make AA your airline and use it's mileage program for the upgrades. AA domestic upgrades are easier with bigger F cabins. Better LAX club on AA vs. UA. UA mileage program sucks with an expensive award chart and partner blocking.