Summoner is king of solo content for being able to form an instant party of three (yourself, Egi, and Chocobo), and if your Chocobo is specced for healing you can form the trinity by yourself (DPS, Tank, Healer). They also have amazing single target and multi-target damage. Oh, and you can raise other players during battle (relevant for the harder FATES).

MRD and BRD are probably second best for soloing. MRD can output a lot of damage and take a lot of hits. BRD can kite and burst down enemies in seconds.

BRD and BLM actually have the lowest DPS (although with the recent BLM buff I think it's unclear where they fall now). I think it's usually something like MNK > DRG >= SMN > BLM > BRD