Rhapsody will use the original Japanese songs from the PlayStation game, along with new tracks recorded by the original cast. The voice acting outside of songs will be in English. The English musical tracks will not be present due to space concerns. The script is also pulled from the PlayStation release, but the English text has been cleaned up!
As for Disgaea, the same seems to be true. Niida told Siliconera that "All the voice acting is there, but unfortunately, we had to compromise on the dual language and English musical songs."