I agree basically with Rey C. and Harley, but I would like to make some side notes. Is the question "Are women taking over as the dominate gender?" actually the question to consider? In itself this question suggests and confirms there isn't a balance between genders at the moment. But it also suggests this non-equilibrium could or should exist. So for the sake of argument... Should it exist? Could it exist?
Man has been the dominate gender for so many ages and we all know what the consequences where for women. Some could argue that in the centuries past people perceived life in other ways, and that maybe women where content with this non-balanced world and way of life. Even if it meant they were given away for marriage, couldn't study, become a priest or politician. But let's not forget this view on life was plotted out by the ruling gender, men, and not a consensus reached between sexes. Even if a woman could be content with her life, she had no choice whatsoever on how she would live it. For that same reason it would be wrong to have it the other way round where women are the dominate gender deciding what life should be. And even a reason why I oppose extremism in feminism. Let's not make the same mistakes twice.
But could a balance be achieved? Let's start with education and jobs... Apart from the topic that sometimes women aren't equally payed for the same job (which I'm not going further into because it's ridiculous), it can also be noted that women and men still choose an education that is more or less to be considered gender-related. Women would go for nursery, teacher, fashion, etc. and men for engineering, mechanics, woodworker, etc. We do have a choice nowadays, so, why? Because it's in our genes? Or because we are from birth treated in a different gender-related way? It's both actually I think. As a kid I had my fair share of duties in the house but my parents would never ask my sister to put up a painting or me to prepare the food (although we had tasks we did both. And maybe my cooking sucks). Parents may reprimand a girl when she climbs in trees and "acts like a boy", and at school you might have tasks, games, courses... that will be separated between sexes (gymnastics for example) or will be labeled 'male' or 'female'. Last but not least you have the differences in our genes, so women might for example not likely go for jobs that are physical heavy because it is physical heavy. So it will be unlikely there will ever be equality in these choices we make and (cause and effect) equality in our daily life and/or relationships. This might be because in some jobs people work more in shifts, and other are day jobs. So although you might say that the tasks at home should be equally divided as part of this 'balance of equality', sometimes it can't be done.
Politics... There are people who say that management should be a representation of society and therefore some quota should be handled to achieve that, like a representative percentage of women versus men in the government. Or that the posts in the management of a company, a university or whatever should be divided according to this percentages. Although this might look equality, does this mean quality? This could mean that when you have 6 candidates for a post you would ignore the (for example) 5 first ones, who happens to be male, and pick choice number 6, the female, because you need to achieve the quota. Even if it means there were 5 better candidates for the job. Is this equality? But would it really matter to have a government or management that (for example) only existed out of women, if they were simply the best for the job?
Religion... I put it in here just to be 'complete' since there is no reason whatsoever for not having equality between man and women when it comes to religion, but apparently there is... I don't think I need elaborate much on this subject to point out it always has been and still is a male dominated part of our life. I'm not only talking about religion and believes itself here, but the role of men and women as a representative of their believe as well. How many female cardinals are there in Christianity and how many female popes have their been? How many women have been victim of a belief where they were stoned to death because of adultery, or physical mutilated because they are supposed to be virgin or are not supposed to enjoy sex? How many women are still expected to throw themselves on the fire when burning their deceased husband, or are woman number so-and-so in a harem, or even forced into marriage because of belief or society allowing it? An example of the latter is a raped girl who has to marry her rapist to avoid being cast out and live in shame, or being stoned to death if she doesn't because she 'provoked' it and is therefore guilty. Achieving equality in religion would mean a world revolution and is not likely to be achieved in just some decades, maybe even centuries. Not only because we have to point fingers to physical mutilation as 'unequal' (as we do), but we have to point fingers to religion itself as well (as we do not).
Just some thoughts...