My 2-cents:
Both Deathwing's and Bahamut's appearence and destruction of the land serve more as Apocalypse events, however, in Eorzea I'd say the fast and highly violent nature attributed to Bahamut's power plus the fact that even the Gods were unable to help the people, is enough to say that Bahamut did a better job overall.

Deathwing was given two years or more to "destroy the world" and ended up just shifting things around and killing a lot of people, and most just sat around with his thumb up his ass. I also want to point out that Deathwing is a dragon smaller than Midgardsormr.

Bahamut managed to kill a significant portion of the Eorzean populace, tear up the overall majority of the land (weather through use of Dalamud as a grenade as someone eloquently put it, thousands of small energy explosions, and of course, Megaflare. Unlike Deathwing, Bahamut had maybe two minutes (from what we can tell) to get in as much damage as possible before mysteriously vanishing for yet known reasons. Also note that he's around a fourth of the size of Dalamud, which was considered a lesser moon, making him quite large. Also, unlike Deathwing, Bahamut had to be sent out into orbit to prevent his presence alone from screwing up the planet - you know, cause Primals eat Aether... that alone could kill the planet, and I don't believe Deathwing can kill anything just from being there =P

Point is, the is kinda a moot argument, but by going over the most basic information as comparison, Bahamut wins simply because he did just as much, if not more damage in a fraction of a fraction of the time that Deathwing did.