Phantom Force's main use is to force out a minimize Drfiblim, and smash anything that it baton passes to that isn't a normal type. Clefable can Minimize. Phantom Force has lower base power (90 compared to 120). Dragon Rush pretty much ends anything that can Minimize now. On the second turn, it deals damage and can hit Pokemon using Protect or Detect. Phantom Force causes the user to disappear on the first turn, becoming invulnerable to most attacks. Shadow Force is also Giratina's signature move. As for why they made the move, only Game Freak know for sure, but I will list a couple of theories.
Shadow force and Phantom force are two different attacks. Shadow Force hits the target even if it is protected by a protection move, and removes the effects of protection moves from the target for the remainder of the turn; if it hits an opponent that is protected by protection move that affects its whole side of the field, it removes the protection move from the opponent's entire side of the field (even if the protection move would not affect Shadow Force… If the target has used Minimize, Phantom Force deals double its regular damage and bypasses accuracy checks to always hit, unless the target is in the semi-invulnerable turn of a move such as Dig or Fly. Phantom Force cannot remove the effects of protecting moves if it does not affect the target (such as if the target is Normal-type).

For Pokemon X on the 3DS, a GameFAQs message board topic titled "Phantom force > Shadow force".