IT seems the summons are all Tai/Nin Damage and they're all based on your main character's attributes. I've got all purple/blue ones but honestly I can't be bothered testing them one by one just to see how much damage they do - they seem to do roughly the same amount, but as a Blaze it's hard for me to tell since Ignited targets take bonus dmg and I would have to really pay attention what goes on when.

i think when dealing with summons its best to get one that compliments your team combo by extending/prolonging it rather than trying to get a summon strictly for dmg if you do want the extra dmg then i recommend getting a summon that has a x10 chase like chameleon or king of hell (ton ton is meh)

all summons of the same colour have the same stats, so you should be choosing which one to use based on their chase attack that helps to extend your combos

okay, thanks guys! this was a help. i think i know what summons i want for sure now, and i'm sure i wasnt the only one asking this question