Obviously the story where they decide who has to clean up after Bat-Cow.
But in seriousness: one is a company wide event, the other a family crossover storyline. They're so completely different in purpose it's unfair to compare them.
But I would prefer reading Battle for the Cowl. Not much prior reading. Just know the fact Batman has died and the battle to claim his mantle is high in tension for everyone ever involved with Batman
As for reading Flashpoint... I'd rather watch the animated movie. It was done so much better than it's comicbook predecessor
Now that aside, I think flashpoint is a bette read than battle for the cowl although what @tupka said is true, it's not fair to compare them with one another.
Thank you so much, we plan on reading flashpoint, then the lantern stuff, then Battle for cow, then Batman who laughs, then suicide squad, then some Superman stuff.