The three U.S. legacy airlines are also, by nearly any measure the three largest airlines in the world, and since its 2013 merger with US Air, American has claimed top honors for nearly every measure of ‘big.’
But the other two were never far behind, and in fact, each claimed the title in turn: first Delta after its merger with Northwest, and then by United after it absorbed Continental.
And even now that American’s undisputed claim has been set aside, at least for the current quarter, there’s no one winner among the three. Delta has the biggest revenue, with $12.5 billion to American’s 12 and Uniited’s 11.4. But, United flew 73.2 Available Seat Miles to American’s 72.3 and Delta’s 71.8. But American still has more planes than either Delta or United.
If airline bragging rights turn you on, by the way, this Wikipedia article lists many more ways for airlines to be biggest!