Togetherwecan: I think you've raised a valid point, but for this point to be valid, we have to determine what a soul is.
Now, for me, a soul is thoughts, emotions. Chemical reactions and electrical signals in the brain. A brain is merely a computer; it's the signals and reactions that make thoughts, emotions, instincts; that is a soul.
For instance: The male hemispheres aren't as well connected as the female hemispheres, which makes verbal communication less important to a male than it is, overall, to a female, while males often do not understand why females simply don't pick up their non-verbal communication, which plays a much bigger part in male communication than it usually does in female communication. Men don't speak as much, because they're usually not that good in expressing themselves verbally, but make up with this in body-language. (This not meant in any sexual way, but more as full-fledged way of communication.)
However, males, with a male brain, can still think female. It is possible for a male to be very much proficient with verbal expression. I myself love to write, debate, pun around, gossip, chatter.. It's real heaven if I do so with women. However, I have no problems whatsoever understanding male communication. How entire conversations can simply be held with a stare and a shrug, a cocking of the head, a raise of the lip, relaxing or tensing of certain muscles. And there's a beauty in that, too.
Likewise, I know women who are also completely compatible with 'male' language aswell as 'female' language. Yet, these women consider themselves fully female. (While I have to admit I consider myself both male and female.)
Men usually have better insight in distance, pressure, forces, rotation.. Technical stuff. But that isn't to say a woman cannot be just as good in that area. Woman are usually better in debate, let's face it. but that doesn't mean men can't do just as well. Men are usually better in cooperating. But this is only because women can be very aggressively competitive. There's no reason woman couldn't do just as well, really. Woman are often better authors. Yet, men can do just as well. (The reason men are often more successful at this is not that they are better, but because there's some social stigma that woman should stick to writing and reading books about romance. However, I've read a lot of female authors that simply blew my head away.)
So.. Do these inborn knacks determine our gender, while someone of the other gender may, in some cases given time, be equally good at it?
Yes, there are physical differences. Men envy women because they cannot be physically pregnant. Women envy men because men are physically stronger, heal faster and can take more damage. (This is simply an example; it of course does not apply to everyone.)
But do these differences determine our gender?
I think we are what we feel we are, rather than what others think we are. An MTF before having had the nescessary adjustments going to an interview in a male outfit is no more a male than that person is after she had help. She's a woman, regardless how she looks, in my opinion. She just has to get the chance to physically look more like a woman. And then: Is being a woman all about having breasts and not having a pair of socks down your pants? Or is it really in your head?
Yes, it does help to have the opposite sex brain when you're TS. But then again; a brain is just a jelly-like computer. A physical thing. A part of the body. While the pulses and chemicals residing there concern you as a person. Yes, an opposite sex brain does improve on these chemicals and signals. But truth be told: They can be there without.
I myself.. Well, I think I have a male brain. Never had it tested, though I have an extremely small hat-size.

I do, however, have extremely high quantities of both estrogen and testosteron (And adrenaline, but that's something else) in my blood. Constantly. An overactive hypophyse? could well be. I'm planning on having my brain-functions tested soon, anyway.
...But this is getting off-topic... Sorry, lack of concentration.. *blushes*
Anyway; I think you are who you feel. And if part of the who you feel means you do not feel the gender you are, then you're not the right gender.
Quote"Plumming! You always assume sex is about plumming, Fitz! But it isn't; it's about love. Yes, I love you. Yes, I long for you. You know that, I know that. But we both know it's never going to be, because you worry about plumming."
-The Fool, The Tawny Man Trilogy, Robin Hobb.