How does Hans Christian Anderson's The Little Mermaid, differ from its Disney counterpart? Why?

In many respects, Hans Christian Andersen's "The Little Mermaid" mirrors its Disney counterpart. The story's protagonist, a young mermaid and daughter of the Sea King, longs to become human in order to gain the love and affection of a human prince. She goes to a sea witch, who takes her voice in exchange for granting her wish, then ventures up into the human world. However, this is where the similarities end.
As with other Disney fairy tale adaptations, The Little Mermaid was made for young children. As such, many of the mature themes and occurrences were omitted or changed. For example, Andersen's story involves a violent and bloody transition from sea creature to human being:

"I will prepare a drink for you; before the sun rises you must swim with it to where there is land, sit down on the shore there and drink it, then your tail will split and contract into what humans call a nice pair of legs, but it will hurt you, it is as if a sharp sword passed through you. Everyone who sees you will say you are the loveliest human child they have ever seen! You will keep your floating walk, no dancer can float as you can, but each step you take will be like treading on a sharp knife that made your blood flow."

Clearly, this kind of rhetoric would not be appropriate for young children, nor would its visual representation. The discussion of death and immortal souls were most likely taken out for the same reason, as was the sea witch's act of cutting out the little mermaid's tongue. These themes and potential imagery would have undoubtedly led to a PG-13 rating, cutting out (if you'll excuse the pun) a large portion of the movie's target audience.
The biggest difference between the two versions, though, has to do with their respective endings. Disney princess films tend to involve a princess who falls victim to an evil witch or queen, followed by her need to be saved by a handsome and valiant prince. Disney's The Little Mermaid follows this formula, while Andersen's story does not. In fact, his protagonist not only fails to gain the heart of the young prince, she contemplates murdering him, eventually dies, and becomes one of the "daughters of the air." Though there is some semblance of a happy ending (in that she has the opportunity to eventually gain an immortal soul), she does not live 'happily ever after' with the prince, nor does she gain her mortal voice back.