There is a general trend toward strictness in charedi communities, which manifests itself in many areas of law, including tznius. (Among Modern Orthodox communities, people tend to follow the basic rules (headcoverings, usually; shirts past elbows; skirts past knees; no low-cut tops) without a lot of discussion and controversy.) There are some reasons why tznius is one of these areas in which charedi Judaism has become increasingly strict.
Sexual transgressions are not seen as very important in today's Western society (except in the case of rape and adultery). But in the Torah, the Gemara, and later rabbinical literature, these sins are considered to be of utmost gravity.
For example, the Shulchan Aruch (Even HaEzer 23:1) says that masturbation is the worst sin in the Torah (though this may have been intended as an exaggeration -- see here: If masturbation is so bad, why is it not in list of 613 Mitzvos?). The Gemara says that one may not derive pleasure from even looking at the pinky finger of a woman other than one's wife (Sanhedrin 75, Berachos 24a). Even improper sexual thoughts (such as thinking about having relations with a woman other than one's wife) are considered serious sins. See this index of references to modesty in the Gemara: http://www.webshas.org/ishus/tznius.htm
In addition, kabbalistic and chassidic thought has tended to put great emphasis on the importance of sexual purity (keeping one's behavior and mind free from sexual sin). According to some literature in this area, sexual sins are the root of all sin, and conquering the desire for illicit sex is understood to be the key to advancing spiritually and fulfilling the spiritual mission of one's soul on earth. (As an example, see this chapter in Likutei Eitzos: http://www.azamra.org/Advice/covenant.html). Although many Modern Orthodox Jews have an interest in kabbalah, chassidus or other forms of mysticism, charedim tend to be more heavily influenced by mysticism. This is an additional reason for the charedi interest in tznius.
If women dress in an alluring way, it will be harder for men to resist staring at them, which can lead to numerous serious transgressions, including lewd thoughts, masturbation, and adultery.
One common response from outsiders is that "well the men just need to control themselves." Yet every society imposes norms on its members, in terms of the minimum areas of the body that must be covered by women. Such norms are necessary, given the explosive power of sexuality (consider the association between adultery and murder, for example)) and the impulsiveness of many men (and some women) in this area. Even contemporary American society has its limits. Jewish law and tradition has its own specific requirements, which, since they have a divine origin, must be better geared toward human nature than the rules of other societies (at least for Jews).
Under the basic halacha, there are certain minimum rules ("dat moshe"), and according to communal norms in each area, there are additional rules ("dat yehudit," custom derived from the practice of Jewish women). Observance of these additional rules ensures that certain women do not stand out and attract the attention of men. For example, what in one community may seem normal may seem alluring in another. Charedi communities, insulated from wider cultural trends in Western society, tend to develop their own stricter dress norms, which seem to have become stricter over time. This may be the result of the evolution of dat yehudit (as some women adopt stricter practices, others follow) or as a result of rabbinic rulings.
An additional reason for the increasing charedi attention to and strictness in the laws of tznius for women has to do with the structure of these communities. Most chassidic communities are governed by a living rebbe whose advice or rulings are taken extremely seriously. Since the Lubavitcher Rebbe said that sheitels were preferable to other headcoverings, nearly all Chabad women have worn sheitels. Non-chassidic charedi communities also closely follow the rulings of their own local rabbis and community-wide gedolim. Modern Orthodox Judaism, by contrast, is less centralized and more individualistic. Even so, Modern Orthodox Jews have become somewhat more strict about tznius over the last generations as well.
The greater attention to the tznius of women (as opposed to men) can be explained as follows. First, traditionally, Jewish men have tended to dress in modest ways, with long sleeve shirts and coats and pants that are not form fitting. There was not a tradition of men walking around shirtless or with skin-tight muscle shirts. In charedi communities, men actually dress more modestly than the women -- since it is very hard to see the shape of a man's body when he is wearing a coat, and a long beard covers up one's facial features (such as one's mouth, chin and jaw). For this reason, there is not a specific need for clarifying the rules of men's dress. Second, men are more "visual" in their sexuality than women, and often tend to stare at women and have lewd thoughts about them. While women may do this as well, their yetzer hara is not as strong in this area.
A final thought: it may seem that all the effort put into modesty in women's dress is solely for the benefit of men's spirituality and avoidance of sin. Yet the correct observance of the laws of tznius are also of great spiritual and practical importance to women, and helps elevate them spirituality. First, their observance helps reduce the sins of others. Second, it reinforces the cultivation of modesty and humility more generally in one's conduct. Third, when men are not tempted by looking at other women they are more satisfied with their wives, and will be less likely to mistreat, neglect or leave them, and will instead appreciate and honor them. Finally, when women do need to interact with men other than their husbands, as in the workplace or marketplace, the laws of modesty promote a healthy distance between men and women and prevent everyday interactions from becoming sexualized. Even in the home between spouses, the laws of modesty prevent sexuality from being in the forefront of one's consciousness, so that couples may develop their relationship in other ways.