Is it based on a manga and/or anime?
No. It was however, Japan's answer to Titanic/Avatar, in that it's the highest grossing ever domestic movie for its time. Even besting the works of Hayao Miyazaki.
There were two versions, the original "domestic" cut, and a slightly different, shorter, US cut which had remastered sound to use THX -- both of which were released in cinemas here.
That should be enough clues for some one to get it =)