Iirc, the manga was started shortly before or even during actual production of the movie, but completed and published much later. So it's not a straightforward

Iirc, the manga was started shortly before or even during actual production of the movie, but completed and published much later. So it's not a straightforward "based on", in many ways - it's a bit like the latter part of Game of Thrones. But I agree that the manga is better, simply because it has time to fleshen out every aspect of the story.