I've heard from a Japanese-American girl that moved back to Japan around age 9 that living growing up there as a woman was terrible, especially having been exposed to the relatively egalitarian American society.
The culture is totally different. Gender roles in Japan are much more defined. Especially growing up in the US and moving to Japan, I think it would be hard -- regardless of gender. For example, young men have to get their career going in their early 20s and often are stressed out to the max. Young women, on the other hand have a lot more options. Like I said, it's just different.
To answer your question, I'd have no problem raising children of any gender here. I also really like the school system, which I found a lot better than what I grew up with in Canada. Again, very different -- you need to know where you are going by the time you are applying to high school, but then the kids are raised to understand that.
I don't really know what to tell you. Usually people from one culture have aspects of it that they think are really good. Other people from other cultures may actually have a completely different point of view of it. In some ways women in the US (and Canada) are in a situation where it's actually difficult to take on the same role that their mothers or grandmothers did. I've had American colleagues lecture Japanese students about how they absolutely should not waste their lives with the goal of being a stay at home care taker. When I asked those same colleagues if they would say the same thing to a boy who wanted to be a stay at home care giver, they said "Of course not" -- apparently not aware of the double standard.
This is the kind of culture clash that I see, especially between American people and Japanese people. Both sides see their point of view as being absolutely correct. For Japanese women, feminism is generally considered to be a dirty word. It's not that they don't want fair treatment, but they find the way that it is pushed as being completely alien to their culture -- to the point of being morally wrong.
Long story short, a Japanese girl does not have the same values as an American girl. Neither does a Japanese boy have the same values as an American boy. And while both sides will defend their moral choices, they are dramatically different. If you raise your children in Japan to be Japanese they will generally be happy -- I rarely see unhappy children where I live (male or female). The same goes in America. Mix and match? That's where you can get into a lot of trouble.
I hope that answers your question. It's a super difficult one to answer because there are a lot of unspoken assumptions. In many ways Japanese culture is literally morally wrong when taken in the context of American view points. The opposite is also true, as hard as it is for both sides to recognise. I'm in the middle where I can see and understand both, but it's hard to respond to questions (from either side) without evoking hatred. The one thing that American culture and Japanese culture has in common is that they are both intensely moral cultures. There is a right and a wrong and very little middle ground. The problem is that what's right and what's wrong is often very different.
I've heard from a Japanese-American girl that moved back to Japan around age 9 that living growing up there as a woman was terrible, especially having been exposed to the relatively egalitarian American society.