They are both equally important for different but inter-related reasons. You can be a doll or a hunk and screw up socially gender-wise and it's a train wreck because the visual queues were there, and that's the first thing we typically respond to. If the socialization is off it's pretty shocking to have "almost" passed to the world you are presenting to, almost as if they were tricked or purposefully misled. I rather be socially on and getting by physically than the other way around.
I found as I my social ease at being out and about increased with experience I had very little blow back during my "guy in a skirt phase." As you can see I'm not that feme but somehow it works 99.9% of the time . . . and the voice (the d___ned voice), by the end of day I'm struggling to even say "Hi" femininely. That's when my social skills (as a woman) really make a difference, and some of the most beautiful inter-personal exchanges with friends and strangers occur when I'm less than perfect.
Of course, what works for me isn't what everyone else should do. I am very visible professionally and my business has me interfacing with senior executives, board members, politicians and their staffs almost everyday. I also speak often to large groups and am recognized in my field in CA and somewhat nationally. Being shy or hanging back because I'm not the picture perfect American elder-states woman doesn't work for my advocacy for children and families - I'm that trans-lady who seems to always be "on" and has something to say worth listening to. That didn't come easily, but it did happen.
I do like to dress nicely and love makeup, etc. and believe on that front I'm mostly believable. But 6'2", 200+lbs makes for an interesting life. I love it and take what there is to be taken.
Luv ya,
Rachel