The author did a very good job covering all the bases and perspectives and I think answered the questions well. Yes, inside the trans community, transwomen may have a bit of an edge in the privilege arena but outside, in the general public, transmen do better mostly because of passability. The negative stigma is still very strong within the mainstream.
Towards the end of the article, the author touches on something I see all the time, within the lesbian community, transmen are pretty well accepted. Within the gay community, transwomen are pretty much rejected, outside of drag.
Julie and I went on a lesbian cruise a few years back. We saw many "lesbians" who were so male looking they could have passed anywhere. Yet they identified as lesbians. Sure. There's no transgender stuff going on there! They simply deny it. That's because, within both the gay and lesbian communities, if you identify as trans, you're out! But there is no doubt in my mind many self-identified lesbians are really trans. They just won't admit it for fear of being rejected.
So within the general public and gay and lesbian communities, transmen are generally more accepted and would therefore enjoy more privilege.
But... transwomen, especially those who transition late, have male privilege ingrained within them. Not all, but most. They are socially conditioned with male privilege and along with that have enjoyed less restrictions on what they do in their lives. Outside of "Don't do anything girly!" the sky is the limit.
There is no one right answer here because of how one acquires male privilege. And I think to fully enjoy male privilege one has to be conditioned to do so from a very early age.