Very far-fetched comparison. I guess in my (Western and mainly Christian/atheist) city I could find 30,000 Muslim women with headscarf (hopefully not all oppressed) and maybe 30 nuns at maximum, who I strongly assume to be nuns voluntarily.

Not far-fetched at all as there are plenty of Muslim women who choose to wear a headscarf without being forced. And why is it that only Muslim women are oppressed? I very much doubt that most Christian women are seen as equals to their male counterparts. Most women still earn less than men, are excluded from certain jobs, etc. Women are still fighting for equal rights. Decisions made by men for women. That pretty much says it all.

I'm the last one to deny that there is still inequality between men and women. But you are not seriously saying the degree of inequality is the same in all countries no matter Muslim or not, are you...