Some Pokemon got really gypped in terms of animations and such for Amie and for general battle. You got Pokemon who have idle animations that play every now and then (Scizor will taunt by clicking his claws, Mewtwo swishes his tail even more, Alakazam will stretch, etc), and those with more Amie animations (Eevee will lay down and roll over, Arcanine jumps like a puppy, Gengar has two dances, Ninetales will lick itself, Delphox will dance, Magikarp will dance, etc).
But then there's the Pokemon without battle idle and their Amie animations are limited to the basics. I want to high-five my Hypno! I want to high-five Mewtwo, but he's too cool for that. You let them idle and they stare at you. Or in battle, they just... don't do anything.
I don't know... some Pokemon got shafted in terms of what they can do.