The only mage stat that doesn't do anything for BLU is the only stat they cannot get. Weapon damage.
All other stats effect them just the same as any other caster. Only, they get bonus value from Int to make up for their lack of weapon damage.
Outside of this, a potential reason for long fights in Masked Carnivale can be due to incomplete rotations. Since, for full damage output BLU would like to use Song of Torment (From Pharos Sirius), Eruption (From EX-Ifrit), Shock Strike (From EX-Ramuh) and Glass Dance (From EX-Shiva) the latter 3 having depressingly low learning rates. The difference these can make is enhancing your total DPS by 50-100% (I.e. Going from ~300 DPS to 500-600 DPS)
As such, popular tactics are to just cheese everything by using Moon Flute + Bristle + Off Guard + Final Sting/Toad Oil + Peculiar Light + Self Destruct where possible to instantly kill some of the stages. In lieu of farming for the skills to fight them properly at a reasonable pace.