I love the varying moves within a specific pet type. I think of the pet as far more versatile if I can use it against multiple opponent types. In PvP, that is a necessity since you never know what pets the opponent is coming at you with.
But even for tamer dailies this feature is great! My favorite thing to do is bring an aquatic pet with a non aquatic move to the daily tamer battle in Deadwind Pass. She has 2 undead pets and an elemental and my Yellow-Bellied Bullfrog
(P/P) has a strong aquatic move Frog Kiss
against her "Jack" and has a strong undead move Tongue Lash
against her two undead pets. And to top it off, the undead are weak against aquatic pets. I love that my frog has an alternate family move for this reason. I have other situations too with the tamers, but this is my favorite because I discovered it purely by accident.