We checked in with the animation team about whether or not races will have different animations and they said that there aren't any plans to have unique animations per race. Instead they'd rather show the uniqueness of each race through their emotes rather than their battle animations. They did say however that they are trying to create unique animations for many of the class and job actions by the launch of A Realm Reborn. Please keep in mind that there is a possibility that they might not be completed in time but that they will do their best!