I see the similarities.

They would have a lot in common the big one is not marrying who their parents pick

this is a no brainer

they obviously have the most similarities, and if anyone has seen Pocket Princesses, they are always together in them, usually questioning the other princesses.

^^ Yeah, but in Pocket Princesses they rival each other and sometimes they're together in a friendly way. Most of the time not.

I don't think she'd go well with Mulan as she would be with Jasmine. It's obvious that Jasmine is a lot like her. Not wanting to marry without decision, they're also both kind of a rebel. They do some useless things that get them in trouble but make them human. Mulan doesn't do those kinda things. She risks selflessly, and all her other acts are disapproved only because of society making a HUGE deal about it. I honestly don't see Merida having any other common act with Mulan other than the fact that they're both tom-boys.

Or Ariel. Merida shares a lot of personality traits with both Ariel and Rapunzel. Longing for freedom, rebelliousness, the need to do their own thing. They'd get along well. I don't think Merida would get along very well with Pocahontas or Mulan, as Merida is less family based or romance based and more selfish, and more reasons.

I think Mulan. They are have a lot of similarites

I always have a problem when Mulan is described as tomboy feminist. Yeah, she goes to the army, but only because she wants to rescue her father. She doesn't like to fight and be a soldier (until sequel, that I don't considered).
I choose Rapunzel. They both looking for freedom and are some 'rebellious' princesses.