The idea of gender complementarianism forms the basis of the "New Catholic Feminism" movement, and many argue that complementarianism is not only feminist, but values and honors women more than traditional feminism. Throughout my academic career, I've done quite a bit of research on gender complementarianism and New Catholic Feminism, and I firmly believe that complementarianism is no more than classic patriarchy.
Here's how Rachel describes it:
Complementarianism (also known as “soft patriarchy”): Christians who identify as complementarians believe that the Bible requires Christian women to submit to male leadership in the home, church (and, according to some*), society.
[*JI Packer, for example, wrote in Recovering Biblical Manhood and Womanhood that “a situation in which a female boss has a male secretary puts a strain on the humanity of both...” Not all complementarians would agree the hierarchy between men and women extends beyond the home and church.]
According to the Council on Biblical Manhood and Womanhood, complementarianism “affirms that men and women are equal in the image of God, but maintain complementary differences in role and function. In the home, men lovingly are to lead their wives and family as women intelligently are to submit to the leadership of their husbands. In the church, while men and women share equally in the blessings of salvation, some governing and teaching roles are restricted to men.” (See also: “The Danvers Statement.”)
Egalitarianism (also known as “mutuality”): Christians who identify as egalitarian usually believe that Christian women enjoy equal status and responsibility with men in the home, church, and society, and that teaching and leading God’s people should be based on giftedness rather than gender.
According to Christians for Biblical Equality, egalitarianism holds that “all believers—without regard to gender, ethnicity or class—must exercise their God-given gifts with equal authority and equal responsibility in church, home and world.”**
[**Note: While I identify myself as egalitarian, I do not necessarily agree with every position/theological rationale of the folks at CBE. And they would probably want me to say that my views are not necessarily reflective of theirs.]
There have been many great posts in the series, which you can read by searching Twitter using #mutuality2012 or by checking out Rachel's blog.