I decided to update this with a poll including the "princesses" that have debuted since. My personal ranking:
1st Tier:1. Ariel / 2. Tiana ~ Really hard to decide. I think Ariel would ultimately win out for several reasons, but I love both characters a great deal. TLM is a better overall film than TP&TF, but I like Tiana herself about equal to Ariel. I think their one similarity is that they're both incredibly driven and both questioning of the people around them (Ariel's smirk when Sebastian sings "Under the Sea" and everything with humans naturally; Tiana mocking Naveen for being a layabout), despite being a friend to anyone--like Tiana with goofy Charlotte.
3. Anna ~ I personally prefer her of the
Frozen sisters, although I love both. I know that’s not a common opinion. I think it’s sort of a Sam-Frodo situation. Elsa like Frodo is the one the plot centers around and also the one with the more glamorous role; Anna like Sam is the one that follows the former around as their average companion who brings them down to earth when they’re overwhelmed and self-harming themselves out of a desire to help others.
4. Cinderella ~ She will always be the best Walt princess and has one of the prettiest gowns in a Disney film (although I’ll always prefer Tiana’s bayou dress).
5. Elsa ~ So pretty and atypical for a Disney princess. Hence her popularity.
6. Pocahontas ~ I like the character more than the movie she comes from. Not that I hate
Pocahontas, just not as fond of it as others.
(Reflecting on my favorites, I think, aside from Anna and Ariel, I generally prefer the more mature-acting princesses?)
2nd Tier7. Rapunzel
8. Mulan
9. Belle
10. Snow White
11. Moana
3rd Tier:12. Jasmine
13. Merida
14. Aurora
Feel free to add heroines to your list; polls only allow 15 options which is why I included the princesses only, but I left the option for others there. Megara would rank after Ariel and Tiana for me.

And Charlotte probably after Anna.

The few moments Charlotte is being serious rather than comic relief, she's such a sweetheart. Nani is another non-princess I really enjoy. She's always been the best part of L&S for me.