They definitely respect each other as equals, but the movie's end scene with the two kind of confirms that it's Mulan imo.

Personally I think she'll gladly let Shang dominate but it is mostly equal.

This one is very equal

At the beginning of the movie, Shang
As the movie progresses, Mulan

Easily. Mulan works better as a helpmate than a leader and seems to prefer it that way too. she can be a bit timid at times too, going along with her humility.

btw, it's not about equality, guys. obviously everyone is equal. but that doesn't mean of two equal people one can't be more forceful or assertive than the other.

Mulan is was raised in the most conservative culture of all DPs. I believe that the society and the family more or less influence every person. And I don't see Mulan as a person who hates everything about her culture. I think that she likes a lot of things( not everything) about it. I think that she would willingly submit to a masculine man whom she love. Sure, she wouldn't want to marry tyrannical, abusive and mysogynist man ( like Chi-Fu) and have no voice in her family. But she values traditional masculinity IMO.