I actually love Mediators and they are great for altering Bravery and Faith stats.

On topic...

I do use Chocobos cause I love watching my knights and Dragoons ride them and the movement boost is a major thumbs up. Byblos is also pretty decent considering your get him so late in the game. Behemoths and Dragons would be fun to use in a party but mostly I use monsters to have a never ending supply of poaching material.

The PSP version gives you even more of an incentive to use them thanks to Luso's innate skills and the fact that you need a specific monster if you want to get the insane stat bonuses from the Mastered Onion Knight Job class.