Jake Hunter Detective Story: Memories of the Past is not simply a remake of Jake Hunter: Detective Chronicles. The three cases in that game have been re-localized. Three new cases have been added, one of which was made exclusively for Nintendo DS.
There is also a new mode in Jake Hunter Detective Story: Memories of the Past called Jake Hunter Unleashed. These are comedic stories done in a completely different style. Finally, more passwords can be found to unlock short stories and interviews with the developers.
