My opinion on what pets are worth bringing (general PvE) when you don’t choose a pet for looks/roleplaying.
Cats: Lynx, Snow Leopard, Jaguar
Birds: Raven, White Raven
Drakes: March Drake, River Drake
Dogs: all of them
Spiders: all of them
Dogs and spiders are good support pets that keep the mobs away from you or keep them from running. Spiders do less damage and control than dogs, but sometimes you need to keep your pet at a distance. Wolf and fern hound give you as good or better support (hard CC or heal) as a moa, but without giving up as much damage.
Those three cats deal the most damage: snow leopard against moving mobs, lynx against less mobile mobs and jaguar when you use traits for critical damage. Stealth and chill are also good utility.
Drakes are tank pets, but deal some damage too. The cone attacks are hard to hit with, but march and river drakes have reliable F2 skills that give a strong burst of damage.
Birds don’t do as much damage as cats, and have little utility to them, so owls and hawks/eagles are mostly weaker versions of snow leopard and lynx. But the blinds from the raven can be really useful against big attacks.
Don’t know underwater, but devourers deal a lot of damage down there.