Well, I'm going to throw my idea in this heap of good answers.
As far as the anime is concerned, they are both forms of "energy". It's obvious what type of "energy" Aura Sphere is, so I'm going to bypass that. Shadow Ball is a the "energy" that ghosts use to manifest themselves with, but in a solid and damaging form. With this said, if there is a time where the two move collide, they will cause a big boom when they collide.
In the odd mechanics of the anime, I would see this as the most plausible.
As always, in the realm of the games, attack moves simply will not collide with each other. Unless somehow Game Freak wants to troll and put the mechanic in.