In the PC Edition, the Wither will attack mobs in addition to the player. They are supposed to attack every single mob that is not considered a 'dead' mob. (Such as Zombies, Husks, Skeletons...) In the PE, the Wither does not attack any mobs.
STEPS TO REPRODUCE:
1. In Creative or Survival Mode, spawn a Wither while there are also qualifying mobs closeby.
2. Notice it will entirely ignore them.