This very much depends on your personal objectives and the amount you travel. All major airlines have programs which recognize their most frequent flyers with elite status. If you fly ~25,000 miles per year that's typically just enough to earn the lowest level status with one airline. If you fly ~50,000 miles per year that might be enough to earn the lowest status with two airlines, or a mid-tier with one. You need to research the status requirements and perqs at both AA and UA to see if you value either of them.

The other consideration is the ability to combine miles earned by flying with miles earned by spending. You will be able to combine Ultimate Rewards points with United miles, but not with AA miles.

There are parallel considerations for hotel chains. UR points complement Hyatt, but not Hilton.