How similar are they? It’s hard for me to tell, as I’ve only been inside one of the movements/blogospheres. But for what it’s worth, here’s my experience.
Manosphere hates male feminists even more than they hate the female ones. Online feminists hate Red Pill Women, as far as I can tell, in a distinctly different way from Red Pill Men. In both cases, you’re considered a traitor to your sex by your opposition – someone who excuses and encourages bad behavior of the opposite sex. You’re also considered weak, unempowered and self-harming by the opposition.
Feminists follow a mainstream worldview. Women in the manosphere follow an unpopular antifeminist worldview. Actually, the women of the manosphere do not follow a completely unpopular worldview. Feminist understanding of the sexes is taught in the same universities that teach real biology and psychology. The latter clearly state there are biological sex differences. And sometimes, when you talk to people, you will notice they have internalized both views without feeling cognitive dissonance. You might hear someone say “there are no gender differences except genitals, there should be equality between the sexes already” and then quote a news article about some study that found that women are more emotionally intelligent, while men are more stoic. Frankly, the only difference between the manosphere views and real scientists are presentation, nicer tone, and more rigorous standards for finding facts. But the overall direction is the same.
Female feminists are sometimes annoyed by male feminists. Manosphere men are sometimes annoyed by manosphere women. But at the same time, being a woman in the manosphere can get you a lot of positive male attention. A manosphere woman who expresses empathy for men can really warm hearts, and sometimes even attract a manosphere man for herself. I wonder if the same thing happens for male feminists?
For both manosphere women and male feminists, being a big supplicator is bad. Feeling guilty over one’s sex is a good way to irritate people who are provoked by signs of weakness – and those are always around. However, I have so far not seen a manosphere woman who is so desperate to please the manosphere men, and so desperate to meet some list of requirements for being a good person, that she is emotionally crushed by “female guilt” and the inability to meet that list of requirements. I have, however, seen male feminists who have reached that point ( look at that: http://lyall.tumblr.com/post/42767719565 I see it’s called Feminist Guilt. Also, there is this: http://vultureofcritique.wordpress.com/2014/06/13/the-social-role-of-scapegoat-and-the-internal-feeling-of-depression-feed-on-each-other/ ).
Male feminists are sometimes accused of acting like a feminist to get into women’s pants. Manosphere women are sometimes accused of entering male spaces so they could be big fish in a small pool. How true is it? I don’t know. But there is nothing wrong with trying to get in someone’s pants, get a partner, or gain popularity in the blogging world. If you can do that AND do something good for the opposite sex… why not?