Honestly, not as much as it used to. I think it only affected my top 3, to be honest.

A little, yes.

well, let's compare

1. the little mermaid--->ariel
2. mulan----> pocahontas
3. BATB-----> Belle
4. Snow White & 7D----> Jasmine
5. Pocahontas----> Snow White
6. Sleeping Beauty--->Mulan
7. Aladdin---->Aurora
8. Tangled----->Cinderella
9. Cinderella---->Tiana
10. PATF---->Rapunzel

With the exception of Mulan & Jasmine, it would be my guess that how much I like a princess movie has to do with how much I like the princess too, at least a LITTLE.

It affect in me. But i got the decision of my favorite princess for what she is, and not for the movie.

URGH! noooooooooooo!!!!! I always like the originals

But not in the way the question implies - I like a movie when I find the characters in it interesting, and since the Princesses tend to be the main characters, it naturally affects how I like the movie overall. There are exceptions. In "Sleeping Beauty", Aurora may be the title character, but she is not really the protagonist, more the catalyst, the three fairies are important to like. And in Snow White, Grumpy is the most interesting character. Plus, both movies have a good antagonist. Since I look at all the character, my list of fac princesses is not identical with my list of of fav movie.

totally....

1. The Little Mermaid ---> Ariel
2. Beauty & Beast ----> Belle
3. Aladdin-----> Pocahontas
4. Pocahontas ----> Rapunzel
5. Cinderella ----> Cinderella
6. Mulan---> Mulan
7. Tangled----> Jasmine
8. Princess and the Frog -----> Tiana
9. Sleeping Beauty ----> Snow White
10. Snow White and 7D ----> Aurora

Or it could be that how much I like a princess influences how much I like a movie. But if I don't like a movie, I will hardly ever watch it, and I won't grow to like the princess. If I love the movie, I'll watch it many times, and often I will like the princess more each time.
Obviously there are other factors too, and my list isn't exactly the same for both, but there is definitely a strong correlation.