imo, I think pets should be different from one another. Whether it be by default or if a player is allowed to raise them in different ways. I would much prefer a default for any pets other than the Chocobo you get to raise.

For example, would be great if the Behemoth would add a STR and Attack Power boon while fighting alongside you, but when not summoned, it adds to your Defense or VIT.

Bomb would boost your Fire Elemental Attribute and your Magic Attack Potency, and while withdrawn, would still boost your Fire Element and also your Magic Accuracy.

This idea alone would make each pet "somewhat" tied to a certain class, but if you were to add ANY diversity to the pets at all, this is what will happen anyways. I am not sure how this pet system will work at all, but I think it would be pretty nice to see them add to your stats a bit, or at least have outside abilities for Gathering and Crafting classes.