This is my honestly my best guess on who this song is about. Let us break down the lyrics.

"If I could, begin to be, half of what you thought of me, I could do about anything."  This is Ross talking to Pearl about how highly Pearl thinks of her.

"I could even learn how to love." Rose does not completely understand love, but Pearl loves Rose.

"When I see, the way you act, wondering when I'm coming back." Pearl knows Rose is gone, but she still acts like she will be back.

"I could do about anything, I could even learn to love like you." Pearl loves Rose. Rose wants to be able to love like her.

Now "Nothing Like You." Is Peridot's turn.

"I always thought I might be bad." Peridot always sensed what homeworld was doing was wrong, but never was able to rebel.

"Now I'm sure that it's true. Because I think you're so good." Peridot knows she was bad, and she thinks Steven is good.

"And I'm nothing like you." Peridot is nothing like Steven, no matter how much she wants to be.

Let me know what you think, or if you have any ideas for another one of these.