Other than my personal feelings, which are subjective and can't effectively be compared to others, I'd say the big difference is stereotypical gender roles and attributes. I usually say I'm feminine over female because to me, female is biological with the femininity usually assumed. There is such a strong link between sex and gender in the societal collective consciousness that everyone assumes that the two are the same, which is why people don't typically get that that's why transgendered people are the way they are; there IS a difference! So for me, I'm biologically male but feminine gender attributes apply to me more than masculine. And I would say that men can't be women but they can be feminine.
Now getting into the definitions of femininity, you'll probably find a lot of attributes that may or may not fit women, because let's face it, being a woman doesn't automatically make you feminine. FtM's aside, some women just don't fit the definitions for femininity which can include traits that could be considered 'soft' and 'weak', at least in comparison to masculinity. There is also an emphasis on empathy and social interaction. In general, I feel like those things apply to me more than masculinity but do they define me? Well, no. So since it's not biological, and it's not strictly the gender attributes of femininity, then I think what makes me 'the woman that I am' is the fact that I'm not a man. Biologically male (brain structures, etc. aside), but not a man. And I think that gender and gender roles may be dependent on the primary sexes. Some may disagree with me there, especially when it comes to some homosexual couplings. But I think the reason for having a more dominant partner in a relationship is a derivative of heterosexual relationships. It's much like how you can't have night without day, or vice versa. Without a different frame of reference, it becomes the norm. So I think comparing myself to a man, I can see that that's not what I am. We have different gender roles for the different sexes and so we have to fit into one category or the other. And with my feminine leanings and lack of manliness, the obvious choice in our gender binary society is that I'm female. Since my biology doesn't and can't match, I just try to make my appearance match as best as I can. If anything it makes that discriminatory comparison that much easier for myself and others. Not only will my behaviors differ from men but so will my appearance.
I also want to point out that I can relate more to women, perhaps because they compare themselves to men as well, and I'm more on their side. I feel the same resentment towards sexism from men that women feel, I think because misogynistic men (and really most men in general) will put down feminine males at least as much as any other woman. So I feel like there's a solidarity there, and another clear sign that I don't belong in the 'boy's club'. I personally feel empowered thinking of myself as a woman who works with machinery, computers, technology, and her hands in general, because I can indulge in typically masculine activities while maintaining and even asserting my femininity. Some might see me as a male who likes some typically male things, but my femininity and rejection of masculinity is what makes all the difference to me.