Agreed that balance between families leaves much to be desired. I don't think this will be addressed at all until the content is fully restored to TWoW's latest patch but it's still a good idea to provide feedback now. Numbers are not important and can be tuned up or down as needed.
First of all, many family abilities are lackluster in one way or another. Screech works better as a tanking ability than shell shield or bubble barrier do, for instance, and the fact that screech is the personal ability of three different families feels bad for carrion birds, since they deal less damage than bats or owls, and so it would make more sense if it was exclusive to the former with the latter two getting new tools. Savage rend is pretty good because it scales well from melee buffs but is given to a family that already has a strong 10% damage modifier. It would make more sense if an ability that scaled like SR belonged to a family with a weaker modifier to compensate (although right now it is what allows raptors to compete with serpents).
Hyena's packleader is cool but sadly is not enough to help hyenas be more viable. The pack ally spawns next to the hunter (because it is considered their guardian) and needs time to reach their target. Scent of blood works on it but I don't think frenzy does. I am also not sure which pet modifiers (from talents or gear) affect them and they don't use or mirror the normal hyena's bite or dash. Obviously, they're not affected by Kill Command either. This ability would need a bit of fixing in the points outlined above.
Hunter-pet interaction is also lacking. What if Kill Command had different effects depending on the family? For instance, each KC used by a hyena could reduce the CD of packleader by some seconds or increase the damage of the next bites/autos by a specific amount as shadow lifesteal for bats. Bestial Discipline should affect all pet abilities and the focus regeneration could be increased and/or given an additional effect of providing 5/10 focus to the pet every time the hunter crits like Go for the Throat from TBC, for instance.
The BM talent tree is also bloated with 5-point talents and has a whopping second to last row with a maximum of 9 talent points. Talents such as Ferocity or Frenzy should be reduced to 3/3 talents while keeping the overall boost. In regards to Ferocity, it'd be interesting to change it so that it adds a flat crit % to the pet (let's say 4/6/8%), and then additional crit based on the hunter's melee or ranged crit (10/20/30%), whichever is highest. Right now, pets cannot scale from the BM hunter's crit or haste in any way.
Family modifiers are also mostly irrelevant. "Defensive" pets barely have more hp or armor compared to normal or DPS ones and so the damage modifier is usually the one that matters the most. Another Classic+ server has tried leaning harder on them and even created custom ones (see
https://vanilla-plus.wiki/index.php?title=Hunter_Pets) so this could be another avenue for unique pet niches or strengths.
While my post has primarily focused on BM, pet families being more useful for MM and SV should also be considered. The moth is a good example of this, as pollen burst can come in handy regardless of spec.
The whole point of this feedback is not to homogenize pets but to find ways of giving families more niches. Ideally, there should be several families fighting for competitive or almost competitive damage. There will probably always be one or two mathematical winners but the difference should not be as stark as it is now. We should be able to use more families for PvE DPS, PvP or other (niche or not) activities.