Actually I'm not done comparing the Little Mermaid and the Last Unicorn, because their stories are actually a lot more similar than people realize. I'm going to talk about the Hans Christian Anderson version for this, because as much as I love the Disney version, it drops the theme of the second transformation.
See, the Little Mermaid does not die in the original story. If you don't believe me, go back and reread it.
"Speak you to the daughters of air?" was the answer. "The mermaid has no immortal soul, and can only acquire that heavenly gift by winning the love of one of the sons of men; her union depends upon union with man. Neither do the daughters of air possess immortal souls, but they can acquire them by their own good deeds. We fly to hot countries, where children of earth are sinking under sultry pestilential breezes- our fresh cooling breath revives them. We diffuse ourselves through the atmosphere; we perfume it with the delicious fragrance of flowers; and thus spread delight and health over the earth. By doing good in this manner for three hundred years, we win immortality, and receive a share of the eternal bliss of human beings. And thou, poor little mermaid! who, following the impulse of thine own heart, hast done and suffered so much, thou art now raised to the airy world of spirits, that by performing deeds of kindness for three hundred years, thou mayest acquire an immortal soul."
Did you get all that? These are creatures that live in the element of air, that like mermaids do not inherently have souls (so they're not ghosts) and have their own society and mission. She undergoes another transformation into a completely different elemental creature, which can be taken as a metaphor for an afterlife, but in text is not one.
Coincidentally, she can earn her soul after three hundred years of service, which happens to be the natural lifespan of a mermaid.
The Last Unicorn also undergoes two transformations. The first time is to escape the Red Bull, whom she cannot fight against as she is, and is doomed to become his final victim cast into the sea if she remained unchanged.
As a human, the unicorn does have her ill-fated romance with the prince like the mermaid does, and she learns some very important lessons from this. Love, grief, regret and rage.
It took a unicorn with the emotions of a human to actually stand up and fight against the Red Bull, something no unicorn has ever done.
The mermaid and the unicorn both undergo a second transformation. They have lost who they once were and can't go back, but they both change into something new that achieves what they originally wanted while they were their original selves.
They change. They live. Coming of age and finding romance are fine and dandy, but that's not what happens when we lock in and find out who we are.