I don't think the airport fight was ever serious from the moment it started.
Until Rhodes got shot out of the sky.
For me, Civil War's final battle easily, I mean easily, outdoes the Batman vs. Superman fight, because the stakes are there, the history between Stark and Cap are there, the history between Cap and Bucky are there, and everything is tied together perfectly between Cap's undying loyalty to protect his best friend (who is also is one remaining connection to his previous life), Stark's rage and general distrust against Bucky, and the entire theme of accountability that's pervaded the film up to that moment. Yes, Bucky killed all those people - but should he be held accountable for it like the Avengers?
Such an interesting and tense final battle, and the action was no less fantastic. The moment where Bucky pushes Tony back against the wall and starts trying to rip out his chest reactor is amazing. The music really helped, in my opinion.
Batman vs. Superman was just lol random inconvenience, plus kitchen sink. I didn't really like either character so it was just a couple of super-powered goons duking it out from my end.
Kind of like if a friend tried getting you into a show or movie and made you watch a fight scene, for example. You don't really give a shit about either character, haha. Sure, the visuals are nice, but that's really all it amounts to.