Does Dragon Ball: Raging Blash 2 Limited Edition have the original music?

Short answer: No. It's all going to be the same music.

Why?

The main composer for the raging blast games, and most of DBZ Kai (right up to the Cell games), Kenji Yamamoto, had been hit with a copyright suit for most of the music he composed.

This initially occurred in May 2011, with Koei releasing a statement with the following:

The existence of multiple suspicious musical pieces which may infringe on the rights of third parties has been confirmed within the musical compositions recorded for “Dragon Ball Kai”, an animated television work produced by this firm. The relevant musical pieces are used as background music in “Dragon Ball Kai”, and measures are promptly being taken to replace the relevant musical pieces from the background music of “Dragon Ball Kai”.

Also, we are proceeding with a swift investigation of the facts, and discussion of countermeasures with concerned parties in the near future.

Almost immediately after this, repeat episodes of Kai had all the music replaced, the games had their music replaced, and it even went so far as to have Toei remove him from their list of staff, and Kenji to denounce any credit for music made for DBZ

Some of the musical comparisons that were included in the claim, as well as a retrospective can be found here.

In the end, this caused raging blast 2 to lose the right to use the Kai music, and instead use the Budokai Tenkaichi 2 soundtrack (as stated on the wiki), which is going to remain the only soundtrack you can hear (unless you find a copy of the game before the suit)