I don't know too much about the church... but I think it's sort of the same. Roman Catholic, Greek Orthodox, etc are more stringent with the separation, or rather purposes of the females in the family, of men and women to the best of my knowledge. But denominations like Episcopalean, Unitarianism, etc are more modern derivatives of Christianity and don't recognize many beliefs of Catholicism.
I have a few friends my age that practice Greek Orthodox and they are in no way comparable to their Mothers... in the sense they have jobs, are treated as equals in a relationship, are not expected to be barefoot, pregnant, and solely running a household unless they so choose. It's amazing how even one generation has changed.
Another difference is in Orthodox Judaism. Women do not sit with men, rather sit in the back of the temple, and in Greek Orthodox they can sit wherever they choose. When I went, we sat near the front and it was the most beautiful church and service I'd ever attended. Even when I went to the Basilica at the Vatican, women were intermixed with the men.
You are absolutely correct about Islamic faith. It's mired very much towards archaic treatment of women. Fully covered unless in the company of your immediate family, husbands only requirement for being a polygamist is to provide equally, devotion and financially, for each family... but good luck proving otherwise... and good luck trying to ever divorce your husband.
Like all the 'orthodox' (for lack of a better way to differentiate) religions, I think particularly practiced within the US there is more equality within the relationship, but often the man may have the final decision... not unlike a 24/7 relationship.
I wonder if it's because in these cultures women are never the providers? It's only been a couple generations since some women have become the financial breadwinner in the family in the US...
In China with the birth restrictions (only one child) if the first is a girl, she will probably be put up for adoption. *shrugs* It's viewed almost as a failure for not being able to provide a boy as the first born. And if a second child is born... if that child is not put up for adoption, there's huge financial fines making it near impossible to pay the government and your bills.