So just for fun I decided to stick my black mage in the same gear my Blue Mage had on and desync him to level 50 to do some comparisons. Ilvl is 111 with black mage also having a store bought level 50 staff.
Black Mages standard fire attack hits for a flat 100% more targets in comparison to Rams Voice or which 130 potency attack you want to use, with Off-Guard on the target and black mage being in three stacks of Astral Fire. Blue Mage casts .5 seconds faster but even in the optimal situation of Off-Guard and Peculiar light, Blue mage was only hitting 75% of the damage of the black mage. Blue mage has better control of burst damage utilizing Primal Abilities but Fire Starter and Fire 3 coupled with Black Mage just plain hitting harder put Blue Mage far behind Black. Blue Mage AoE is both better and worse than black mage, with Rams Voice into Dragons Voice destroying mobs but Fire 2 dealing more damage to multiple mobs in the event that Rams Dragon wasn't available. Primal Abilities also pushed Blue Mages AoE up even further beyond the black mage.
Bristle not being usable with the Primal Abilities hurt. Explosion, 220 potency, only hit for 1000 damage with a target being under the effect of Off-Guard. Comparatively speaking Fire 3 is 240 potency, hits for upwards of 1600 with the same gear. Yes, multi-target versus single target, but even with improved Main and Mend with Off-Guard up, there should only be a 10% difference in damage, not a 50%.
A Bristled Rams Dragon peculiar light combo was able to hit consistently around 2700 damage but that is entirely dependent on the target not being immune to deep freeze and on Peculiar light being up.
Finally yes, I am aware that Blue Mages have a variety of status attacks no one else has access too. Those skills are entirely dependent on the target not being immune to those status effects and in my soloing of Arum Vale I discovered that even the first boss of that place was immune to everything but Poison and Damage down.
Two things in summation. The first is that Blue Mages can absolutely wreck normal mobs and trash mobs in dungeons but are fairly pitiful against bosses. Second is that I think it was Pheonix who said it, was right. The lack of a dedicated main weapon and the damage ((And defensive stats, my black mage had almost a thousand hit points more then my blue)) stats associated with it really seem to be holding the job back.