>We have a good approximate idea of male and female gender in our society.

Which is... ?

>If you were magically transformed into a woman [...] You have no particular identification with being a dude?

But with my memories still intact? To answer this question I need to give some background. I believe the "gender" concept of "man" and "women" are drawn from the sex differences between male and female in humans. The most important aspect of which is hormonal differences, but also the physical weakness of the female compared to the male. Then, on top of this, there is a second order cultural effect that will dictate how this difference is expressed. But those societal differences would go away in one generation if the sex differences went away. And the societal differences are varried across cultures. But these societal differences (what one might call gender) are the result of already being a male or female. That is, the societal differences are taught and learned, not deduced. So "gender" is not a choice. For example, if a group of children were to be raised away from society and the people raising them treated the children exactly equally none of the children would have any gender. That is, there will be no additional enforcement of the already natural sex differences, which are already large. In fact, the females would be more feminine than liberal-raised females who are explicitlty nudged against their natural tendencies.

All this is to say that your question is difficult to answer because you are asking what would a female do with male memories? Would the hormonal differences win out over these memories? You're asking a question that can't be answered. As for me myself, I wouldn't be myself, because the neural architecture is different between sexes. (At least to some extent. Compare the rate of autism between males and females, for example). If we assume no neural change and no hormonal change, that is, I get to keep my testosterone, I'd probably become a female athlete of some sort. But the case you gave wasn't clear about how much "male" is left after I become female. At face value it means I only keep memories. If that's the case, there is a chance I would just ignore the aspects of the memories that would tell me to stay male.

I should note that the opposite case - a boy[0] who's parrents where convinved by John Money,[1] the originator of "gender," to raise him as a girl after a botched circumcision, eventualy committed suicide. So I don't think this will be an exactly pleasant situation either way I choose.

>If you had the ability to transform back you wouldn’t do so because you’re a woman now and women aren’t men?

I probably would, because of the memories, but you didn't give that option. Perhaps if the option was given after lets say 5 years then "I" wouldn't but I don't know, because I wouldn't be me. This was a really complex (and rather useless) case to answer "what is the difference between a man and a woman." Even given the difference between a man and a woman this is still a hard question to answer at all and one that is impossible to answer absolutely.

[0] https://en.wikipedia.org/wiki/David_Reimer

[1] https://en.m.wikipedia.org/wiki/John_Money