does it make a huge difference on witch one I use? or does one family of pets just way stronger than the others?
The only way it makes a difference is if you’re the sole provider of Bloodlust to your group then you will need a Ferocity pet.
Otherwise all pets do the same damage so it’s a utility choice depending on the content.
Damage is normalized, so that doesn’t really matter.
I use specific pets based on other mechanics. In fights where you need more health, choose tenacity. Need movement speed, choose cunning. Need Bloodlust, choose Ferocity. Need to slow targets down, choose a pet with snares. Need mortal strike effect, choose a pet with Mortal Wounds.
It depend on what you’re doing. For open world/solo content you’ll want Ferocity for the leech.
For PvP it’s usually Cunning for the speed boost.
As for Raids and Dungeons, it’s situational as Tenacity gives you extra health if you need that, Ferocity gives you a Bloodlust if that’s needed, and Cunning gives you a speed boost if you don’t need either of the former.
As stated previously, they all do the same damage.
They always expect that we have a lust pet. Raid leaders will say to lust followed by “HUNTER”. Most groups bring hunters just for that.
Raids will probably already have a Shaman, Mage, or Evoker so in those cases they should let the Hunter use a Tenacity pet because it will be better for survivability in raiding.
Granted, I have been in raids with plenty of Shamans and Mages yet still I’ve had to cover lust. Usually they are pretty bad raids or battlegrounds though.