What's the "best" AoE classes in the game for specific situations?

[Sleigh]

First things first, I know there are a lot of specific elements to consider, such as possibly having Bards in your party to regenerate TP/MP, or how long the encounter lasts (20s encounter vs 200s encounter will have drastically different results), what level of gearing you are for the content, etc.

Taking that all into consideration, what do you feel the best AoE classes are for dungeon runs, for Bahamut's Coil Turn 4, and just in general bursting down adds? Playing a BLM, I know my AoE capabilities are strong both in burst and in sustained, but I don't know about how other classes stack up, especially with nigh-infinite TP. What kind of Potency Per Second can the classes boast for AoE?