Many directors of Shakespeare films have not been great film innovators and stylists—they've been stage directors with a deep understanding of the plays. That combination is enough to produce a great Shakespeare movie. But there's another group of directors who have both a deep understanding of the plays and who are also great film stylists and innovators.
At the summit of that group are two directors: Orson Welles and Akira Kurosawa. Welles had directed most of Shakespeare's history plays by the time he was fifteen, and he reread the plays throughout his life. His three feature-length Shakespeare films are the best things he ever did. He thought, and I agree, that his greatest film wasn't Citizen Kane but The Chimes at Midnight, his mash-up of the Henry plays.
Similarly, Kurosawa's appreciation of Shakespeare began early, when he was an art student, and continued throughout his life. Three of his best films are versions of Shakespeare plays. The Bad Sleep Well loosely follows Hamlet, resetting it in contemporary Japan. Ran ("Chaos") is an adaptation of King Lear set in feudal Japan. And Throne of Blood is a Macbeth adaptation, also set in feudal Japan, that follows Shakespeare more closely than either of the other two films.
Still, Throne of Blood changes Macbeth in a number of ways. Most important, Kurosawa's Washizu is not as evil as Macbeth, and his Lady Asaji is more evil than Lady Macbeth.
Let me give you two examples.
First, Lady Asaji manipulates her husband into murdering the Great Lord (Duncan) by saying that Miki (Banquo) might reveal the prophecy that Washizu will become Lord of Spiderweb Castle. If the present lord hears this, he'll consider Washizu a potential usurper and have him killed. Washizu launches a preemptive strike, killing the Great Lord in part to keep himself from being killed. His defensive action differs dramatically from Macbeth's killing Duncan out of sheer ambition.
Second, in Shakespeare's play, Macbeth decides on his own to kill Banquo and Fleance; he keeps his exact plans secret from his wife, saying, "Be innocent of the knowledge, dearest chuck, / Till thou applaud the deed." In Throne of Blood, far from wanting to kill the Fleance character, Washizu wants to name him his heir. He and Lady Asaji don't have any children, and Washizu wants to reward the Miki's loyalty. Lady Asaji talks Washizu out of this plan in words that echo Macbeth's soliloquy at the beginning of Act Three: "To be thus is nothing / But to be safely thus." She finally encourages Washizu to kill Miki by saying that she's pregnant, that their own son could become the Great Lord. Washizu is thus manipulated into murdering his friend, rather than coming up with the idea on his own.
Kurosawa's overall idea of the character is reflected in the title of his film, which in Japanese means not Throne of Blood but Spiderweb Castle. Spiderweb images occur throughout the movie: in the bare trees in Spiderweb Forest, in the spinning of the "evil spirit," and in the web of arrows that surrounds Washizu at the end of the film. These images point to Kurosawa's sense of the main character as a man largely caught in a web woven by others, rather than a man who, tempted by others, weaves his own web.