Falcon's aerials more often than not aren't aerials. The majority of Falcon's moves involve his "aerial" moveset, but they are almost all SHFFL'd, which makes them more like ground moves, they're just faster, more powerful and have better range. But make Falcon fight in the air, pulling off whole combos without landing, and he loses his edge. He has no control once he's in the air; once he has a direction, that's his direction, and when this happens, Jigglypuff will destroy him, because she can go wherever she wants in the air. Once Falcon lost his second jump, Jiggs would control the game.
As far as I'm concerned, the top three characters at aerial fighting are Jiggs, Peach and Samus, based on their ability to maneuver in the air, their ability to control an aerial fight, and the options that they have for aerial finishers. I think this is why these three are characters whom you edgeguard by waiting at the edge, and do not engage aerially, because they can turn an aerial fight around in a split-second.