How are Children of Men and Hamlet similar and different in terms of feminist criticism?

Hamlet and Children of Men are similar in that both address the feminist concern of patriarchal hierarchy, which accounts for the domination and power of men over women and over society at large. This domination manifests itself through subjugating women, rendering them powerless and voiceless outside their prescribed roles of nurturing and purity. Hamlet and Children of Men are different in that P. D. James subverts the notion of patriarchal hierarchy by making men physically and intellectually impotent—powerless—and the cause of global society's destruction, both symbolically and literally. In James's fictional world, a new child has not been born for twenty-five years.In a distilled overview of a few key points, feminist criticism holds that central to literary (and corresponding social) issues is the patriarchal power struggle; men dominate the hierarchical power structure and so dominate women and society. This leads to another key point, which is the marginalization of women. Women spent thousands of years being seen as insignificant and voiceless outside their prescribed and constraining roles as child bearers, child raisers, and nurturers of society. Women's roles introduce another key point—that of the patriarchally requisite and mythic purity of women. This contrasts sharply with the patriarchal view of men for whom battle and struggle against each other for power (in any personal, social or political realm) is accepted as requisite.In Hamlet, the central problem is the power struggle within the patriarchy of Denmark. The hierarchical struggle manifests principally as Claudius versus the now-dead King of Denmark, Hamlet's father; as Hamlet versus Claudius (uncle and new king); as Laertes versus Claudius (and then versus Hamlet); and as Fortinbras versus Denmark. Hamlet's hierarchical struggle first manifests as he mixes rage with grief over Claudius' usurpation of the throne and Queen (Hamlet's mother) and, second, as he mixes rage with incredulity, confusion, and indecision after receiving the Ghost's instructions. In the midst of these struggles, the women, Ophelia and Gertrude, are marginalized, manipulated, and disparaged. The main effect on Gertrude is that she questions Hamlet's sanity, representationally questioning the soundness of Denmark's patriarchal order. The effect upon Ophelia is demonstrated in her descent into madness (essentially over grief that the man she loved, Hamlet, senselessly killed the father she loved, Polonius), as well as in her seemingly accidental—though self-inflicted—death: with no resort to voice, her resort was to flowers, games, and childlike songs:

There, on the pendent boughs her coronet weedsClambering to hang,. . . herselfFell in the weeping brook. . .Till that her garments, heavy with their drink,Pull'd the poor wretch from her melodious lay. . .

In the 1992 novel Children of Men, global society is in conflict because men are sterile. James inverts the situation found in Hamlet by making the male patriarchal hierarchy responsible for world collapse: in James' fictional world, since 1995. Worse yet, the patriarchal establishment cannot find out why. Not only is the patriarchal establishment (and all men, as they are adjoined and answering to the establishment) physically impotent, but also men are intellectually impotent to understand why they are impotent.
The women in the novel are still without a powerful official voice—their powerlessness illustrated by Xan Lyppiat, "the dictator and Warden of England," and representative of powers in other "world nation states"— and are blameless. Sperm has become ineffective, not the women's wombs. "Even the frozen sperm stored for experiment and artificial insemination had lost its potency." Nonetheless, the resurgence of old mythology and superstition attributes the loss of potency to women's "witchcraft," the mythological domain of women who reject (or are assumed to reject) the requisite role of purity. While there is a similarity in patriarchal struggles for dominance and power between Hamlet and Children of Men, James turns the whole hierarchy on its head by making men the powerless and "voiceless" ones because they are the physically impotent ones. James also makes the men intellectually impotent to stop the infertility since it is within themselves, and they cannot understand why their physical impotence is generated. James thereby subverts the patriarchal idea that women, the vessels of purity, are equally the corrupters of society, the supernatural witches of society.