This is such an open question that I'm finding it hard to answer without first defining what is meant by "weaker" position. On the one hand, you can say that women are in a weaker position because there is still a lingering tendency for men to treat them as a form of property. On the other hand... women have an inherent value as wives and mothers and as a society we're less likely to send them off to be cannon fodder in needless wars.
For my part, I'd say that the power imbalance would be cis-conforming vs. cis-nonconforming. The closer you come to the extremes of the "cis ideal' the more relative power you have. It's the Chuck Norris' vs. the Woody Allens and the Uma Thurmans vs the Anne Ramseys.
As an example, look at the bullying of gays boys in high school. The bullying is not always triggered by an overt sexual orientation, but by a perception that someone is effeminate. The closeted gay quarterback is less likely to be bullied for being gay then the straight president of the fashion club. The same holds true for girls who aren't 'feminine enough'. They get the same sort of grief for not conforming closely enough to the 'ideals'.
If I had to rank things by relative power, acceptance and opportunity in western society I'd say it's... powerful men, beautiful women, cis-men, cis-women, feminine lesbians, masculine gays, masculine lesbians/transmen, effeminate gays and transwomen. (Your experience of this may vary depending on whether you can pass as another group higher up or lower down the chain.)
Of course this is just a generalization. This isn't the only power dynamic out there. There's rich/poor, extroverted/introverted, talented/untalented... but if we are talking which sex has power in society then macho men and pretty women both have an impressive arsenal.