I don't think she's really defined by her powers. It's her personality and mental strength that make her unique more than anything.

Basically what Aang_Lite said. She is set apart by her powers, but they don't define her, and there are many other personality traits she has that aren't unique at all. (Quirkiness, love of nature, optimism, etc.)

Poeple who think that are just as bad as Mother Gothel, the villain, for defining her based only on her powers and not her personality.

I think it makes her unique between the Disney princesses because she is trapped in a dilemma none of the others has to face. The hair is destroying her life, and yet, she never considers to cut it because she knows that it can also be a good thing. She is practically trapped by her powers, despite the fact that she can control it.

No, that doesn't have anything to do with her as a person (same with Elsa, who people always act like is extremely unique JUST for her powers alone).

Initially, somewhat. But now, there are already lots of Disney heroines who have super powers make her no longer unique.

She's not set apart from the others for her powers, she's set apart for her personality.

Nobody needs powers to be special and unique