I'm beginning to wonder if there's a generation thing here too - I'm more used to the word "gender" meaning simply male/female/other (as well as its more recent application to "sense of gender" or "gender role" from a sociological/experiential perspective) rather than the word "sex" being used for that, when it comes to people.
And I think it's specious to claim that the "sexual" in transsexual refers simply to "sex" as in male/female/other, because in our culture, "sexual" is a profoundly sexualised term whose meaning points towards sexual activity, not gender. I've just started reading Transgender Warriors, and I am more uncomfortable than I expected with the term "transsexual", especially as a noun - because it reminds me of "homosexual" used as a noun (and used as a weapon), as if it somehow defines someone, and defines them purely in sexual terms. It feels really loaded to me, in a way that transgender does not.
I find it significant (but in what way, I have no idea!) that transsexual is the medical term of choice in the US, and transgender is the medical term of choice in the UK. I wonder how that happened.