Hakuouki was both an animated film episode series and a movie series. The animated film came before the movie and was much longer than the movie. The movie was a shortened, simplified, and less thrilling movie, although a small percentage of fans liked the movie more due to it being shorter and giving people more furry powers. (For instance, in one scene when Kasama and Hijikata were fighting, there was electrical currents and flashes of light with each clash of swords.) The movie also changed many, many scenes and made several deaths to be less heroic and less dramatic.
Voice acting For the most part, the voice acting was the same. However, the voices for the two intel members of the Shinsengumi were changed and one character was even cut from the movie.
How the characters dress The Shinsengumi wear a thin layer of armor around their bodies while in traditional uniform, whereas in the anime there wear lightweight clothing which allows them to fight more adgilly. Chizuru's brother wears red in one scene when in the anime he wore black at that point. Various other small changes.
Scenes changed (please add more)
Okita's death - The Shinsnegumi's assassination of the leader of the Guardians of the Imperial Tomb Anime: In the dark, they hid in several shadows around an intersection and then without warning they charged and ran him through. Movie: They surrounded him and then finished him off
Anime: Okita was alone, hiding behind a tree, listening to rouge samurai plot attack the Shinsengumi. He suddenly began to cough up a lot of blood and realized that his tuberculosis was not going to get better. As the rouge samurai put out their lanterns and began to descend down the hill, Okita stepped out into the path, blocking them. They ordered him to step down, and when he refused, they shot him. Due to his fury powers gained from the water of life, he suffered no harm and charged up the hill cutting them down three at a time and fighting all of them, surrounded on all sides and being rushed at by samurai with drawn swords. He was run through once, but suffered little harm and kept fighting. When Hijikata ventured to the hill, he saw Okita's sword planted in the ground in the middle of a road filled with dead enemy samurai. Movie: Okita died in battle from using up all of his life on fury powers.
Kasama's death: Anime: Hijikata heroically charged at him during their duel at the end of the film and put his katana through Kasama's heart. Kasama then acknowledged Hijikata's skill, leadership, and admitted that he was wrong before falling over dead with the katana still in his heart. Movie: Was injured by Hijikata, called an end to the duel, and left.
Ending: Anime: Hijikata fainted after putting his katana through Hijikata's heart. Chizuru rushed to catch him and cried, remembering all the things that the Shinsengumi had fought for, and the movie ends showing the whole Shinsengumi team in the pale blue overcoats, smiling. Some say that Hijikata would have turned into dust if he had used up his life, but it is implied that he died. Still, there's room for you to believe that he either died a hero, or lived on and married Chizuru, whichever you would rather have as an ending. Movie: Hijikata lives, and theoretically, lives the last of what was left of his life with Chizuru.