Click to read Part 1, Part 2, and Part 3.
I warn you that I'm going to be a little harsh on Ariel. The thing is, The Little Mermaid was released 30 years after the previous princess film, Sleeping Beauty. So while you would expect that Ariel moved the whole princess concept into modern times, I'm not always convinced that she did. (Yes, I'm calling the late 80's and early 90's "modern" because these are the films that were new when my generation was growing up--even though I realize that they're now over a quarter century old.)
We must first acknowledge that many things about Ariel are different than with her predecessors. Compared with the others, Ariel looks and talks like a modern girl. If I'm not mistaken, the dresses in this movie would place the timeline vaguely around 1850--Cinderella, though, looks to me like the 1830's or 1840's (I can't remember which). Yet The Little Mermaid feels all around more modern: Cinderella is filled with the fantasy of fairy godmothers, talking mice, and castles, whereas the only magical/fantastical elements of The Little Mermaid are linked with the sea and therefore the "real world" elements of aboveground stand out more. Cinderella speaks with grace and poise in both her tone and vocabulary. Ariel, however, speaks more casually--she doesn't speak like a princess, or even necessarily like someone raised in the upper class. She does speak like a rebelling teenager.
Snow White may be the youngest Disney princess, but Ariel acts the youngest. I find it strange that a team in 1989 decided to make Ariel act more like a modern figure and yet kept her as a sixteen year old who falls in love with a man and then finds a way to marry him. She tells her father that she's sixteen as a way of saying that she is old enough to be treated more like an adult than a child--but sixteen is still underage to us in modern times. So Ariel's age is odd. (Snow White's and Aurora's ages are not so odd because their stories take place in more medieval times and were arguably created before we started analyzing Disney princesses in so much detail.)
I think Ariel is intended to be empowering because she speaks for herself and makes her own choices about who she is, what she believes, and what she does. It's true that it is admirable of her to see the humans as people even though the rest of the merfolk fear them--this is an alright theme of equality among differing peoples. But most of what Ariel argues about doesn't have to do with deep political, social, or philosophical questions. She just wants to be free to swim around without anyone watching her or telling her where she has to be and when--and she is very quick to fancy herself in love with a man she saw once.
Now, I am not demeaning Ariel for this. There's nothing wrong with a youthful falling in love with someone you see, someone who represents something to you that you may or may not realize. And I don't necessarily mind The Little Mermaid's love story: after the first meeting, Ariel does spend enough time with Eric (in movie terms, that is) to get to know him. And it's all very pretty, classic fantasy: the mermaid leaving the sea because she fell in love with a man on land. However. Ariel's crush on Eric (that is, the feeling she had for him before she left the sea) put her into a lot of trouble.
For one thing, it causes her to defy her father. I did always find it harsh and unfeeling of Triton to just destroy everything in Ariel's grotto: that didn't help--it drove her away. But Ariel was perhaps rather naively ignoring her father's warnings of the land, and she talks back to him more than she needs to (out of anger and sadness, yes, because no one is perfect, I realize, but still).
And most of all, Ariel's crush leads her to make a deal with Ursula, a deal that puts herself in essentially mortal danger. Then, of course, Triton trades places with her to save her--which puts him and thereby the entire ocean and all the merfolk in danger. Making a deal with Ursula was extremely rash, selfish, and naive of Ariel. If only she had had more patience, then perhaps she could have met Eric again as herself and even eventually talked her father into seeing her side of things. She could have achieved the ending of the movie without all of that "dark stuff" in the middle.
But perhaps that's the point. Ariel was never designed as a figure of virtue or a representation of royalty. She's just a girl whose father is king. She therefore has flaws to show that she is a real person and to show how people can overcome their mistakes. (Though I'm not really sure how she overcame her mistake. I think the situation healed with the death of Ursula, but didn't Eric do that when he ran the ship into Ursula? Thematically, though, Ariel overcame her mistake--at least because she saw how badly her deal with Ursula turned out.)
It all comes down to what you prefer. Do you want a Disney princess who is like you? Or do you want someone you can look up? If you want to relate to a Disney princess, then Ariel is your type (this figures since so many young and youngish women love to dress like Ariel or take pictures like her and such). For me, though, I prefer a character I can admire. Ariel was an interesting addition to the mix and I do like her movie--but she isn't my favorite of the princesses.