If I had to make a $100 bet today on what future research will find, I would wager that
1. FtM HRT reduces Big Five neuroticism despite increasing aggression. The effect is permanent and persists after the person's "second puberty" induced by HRT is over. It affects beliefs about how society should function. To a degree of approximation, it makes transmen more conservative or right-wing than they were before the treatment.
2. MtF HRT does not have the opposite effect to the above (but it may, and probably does, have other effects). Edit: The opposite effect on neuroticism and sociopolitical beliefs. It decreases aggression.