Quote from Bayushi;183318:
well, i'm new to pets, and thinking of getting the guardian spider as my first pet
Pets dont gain additional stats from rebirthing, because they have caps on skills, and you can only rank skills on them by hitting certain levels, you cannot max all skills by rebirthing them, only by getting to really high levels.
Regular characters though, use ap to rank skills, so it is useful to rebirth, to get more ap, to rank more skills.
If you want a pet, just buy the card for it, rebirthing pets is really only for transfering skills over from pet to pet, eg, lightning bolt from a pet that has it to a pet that doesn't.