Huston vastly improved on Bradbury's script.
Warning: spoilers below.
Ray Bradbury apparently disputed have Huston's name added for screenplay credit, but Huston fully deserved the screen credit he received. Bradbury took out some of Melville's best scenes and words, which Huston wisely put back in. A comparison of the Bradbury's original screenplay and Huston's final product is very revealing:
Dialogue is about sixty percent Bradbury and forty percent Huston. The final talk between Ahab and Starbuck ('tis a mild, mild day) was restored to the script by Huston and also expanded.
Huston let Orson Welles run free with Father Mapple's sermon, so Welles beautifully rewrote it himself.
Bradbury took out the scene of the blacksmith forging a special harpoon for Ahab. Huston put it back in.
Huston didn't like Bradbury's choice of whaleman's songs so replaced them with a better selection and even increasing their number. They are all original to the era.
Bradbury clearly had Moby Dick die in the end. Huston kept it rather ambiguous, just like in the novel.
The idea of Ahab rising from the grave and "beckoning" is merely mentioned in Bradbury's script by Elijah the prophet. Huston brought it to cinematic reality, based on what happens to the book's character of Feddelah who does not appear in the movie. Huston made Ahab literally rises again from the sea and literally beckon to the crew to follow even though he is dead. That's the most chilling moment in the film. This is also the scene that so many people think is actually in the novel, but it's not. In the novel Ahab is pulled overboard by his own harpoon line and strangled to death, he does not drown strapped to the back of Moby Dick while repeatedly stabbing him.
It is quite clear that adding Huston's name for screenplay credit was justified. It is a better film because of his changes.