What the Bible Says
If a woman does not cover her head, she should have her hair cut off; and if it is a disgrace for a woman to have her hair cut or shaved off, she should cover her head. A man ought not to cover his head, since he is the image and glory of God; but the woman is the glory of man. For man did not come from woman, but woman from man; neither was man created for woman, but woman for man. For this reason, and because of the angels, the woman ought to have a sign of authority on her head. (1 Corinthians 11:6-10)
What the Qur'an Says
O Prophet! Tell your wives and your daughters and the women of the believers to draw their cloaks (veils) all over their bodies. That will be better, that they should be known so as not to be annoyed. (Qur'an, 33:59)
And when you ask them (the wives of the Prophet) for anything you want, ask them from behind a curtain: that is purer for your hearts and for their hearts. (Qur'an, 33:53)
The Bible instructs women to cover their heads. The purpose of the covering is to show the authority of men over them because men are the image and glory of Allah while women are the glory of men! Because of this teaching, some non-Muslims think that Muslim women, who wear the veil, are ill-treated and neglected.
Unlike the Bible, the Qur'an instructs women to wear the veil for their protection. The veil is one of the Islamic measures to create a righteous society and to block the roads leading to fornication and adultery. The Qur'an clarifies that the veil makes wicked men stay away from women. Furthermore, the veil purifies the heart from immoral thoughts and temptation because showing beauty may excite men's sexual feelings. On the other hand, the Qur'an allows women to show their beauty to other women, their husbands and some close relatives in addition to children.
More about the Issue of Modesty and Interaction
There exists, among Muslims a big gap between the ideal of the real. Cultural practices on both extremes do exist. Some Muslims emulate non Islamic cultures and adopt the modes of dress, unrestricted mixing and behavior resulting in corrupting influences of Muslims and endangering the family's integrity and strength(see : muslimbridges.com). On the other hand, in some Muslim cultural undue and excessive restrictions is not seclusion are believed to be the ideal. Both extremes seem to contradict the normative teachings of Islam and are not consistent with the virtuous yet participative nature of the society at the time of the Prophet Muhammad.
Parameters of proper modesty for males and females (dress and behavior) are based on revelatory sources (the Qur'an and authentic Sunnah) and as such are seen by believing men and women as divinely based guidelines with legitimate aims, and divine wisdom behind them. They are not male imposed or socially imposed restrictions.
The notion of near total seclusion of women is alien to the prophetic period. Interpretation problems in justifying seclusion reflect, in part, cultural influences and circumstances in different Muslim countries.