I understand that Muslim women have a clearly stated right to property separate from the control of men. (I haven't read the Koran myself, I have only read about this right.) You would be correct if you thought that there is no exact right of that nature given to Christian women.
I'm not sure I think in terms of "rights" given to women, but here are my thoughts:
1) When a Christian woman is married to a Christian man, the husband's body is said to "belong" to his wife not to himself. (The body of the wife in a reciprocal way is understood to "belong' to the husband.) Married Christian couples are also specifically told not to sexually deprive each other, except for a short time by mutual concent. I take these two passages to give a married Christian woman a right to a sexual life with her husband, and that a sexual outlet is not to be withheld from her.
2) Christian men are told to treat unmarried women in the church as sisters, meaning, I think, that Christian men are supposed to take a brotherly, even protective attitude towards all Christian women, not just those who are their blood relatives. This might be taken to mean Christian women have a "right" to masculine help and support from within the household of God.
3) Christian women are given status of equality with men before God with the biblical statement "In Christ there is no male or female...all are one in Christ."
4) In the ministry of Jesus and in the early centuries of the church women had roles of responsibility & influence. I don't know if this could be described as a "right," though it seems very valuable. Perhaps it is the right to be a disciple, and the right to be active in serving God.
5) Widows are mentioned as a group of people who the church should take care of, at least elderly widows. Since no such provision is mentioned for elderly men, it seems elderly women can expect a practical support from the church that is not extended to elderly men.
I wrote a hub about women in the early church here: https://hubpages.com/religion-philosophy/Can-Women...