How do men and women portray mental illness differently, in particular, Plath in The Bell Jar, Styron in Darkness Visible, and Redfield Jamison in An Unquiet Mind? Do you see any differences (based on gender) in how they represent their mental illnesses?

There are similarities in the ways Plath, Redfield Jamison, and Styron portray mental illness. For example, they all feel fraudulent and doubt themselves. Plath, who is living in New York City to work for a magazine, feels envious and inferior to the other girls she works and lives with, and Redfield Jamison feels insecure when she has to introduce herself to fellow students at Pacific Palisades High School. Styron feels like a fraud when he is going to Paris to receive the Prix Mondial Cino del Duca. Rather than experiencing a boost to his ego, he says that "I had suffered more and more from a general sense of worthlessness." For all three writers, their mental illnesses make them feel worthless and insecure.
However, there are some differences between the way Styron, a man, and Plath and Redfield Jamison, both women, portray their illnesses. Styron has long been able to deny his illness and has used drinking as a means of coping. When he receives the literary prize as a adult, he has just realized days before that he is suffering from a mental illness. However, Plath and Redfield Jamison seem to have dealt with their illness from an early age. Plath writes of her depression and fixation as a young woman with the Rosenbergs, who were executed for allegedly being spies, and Redfield Jamison writes of her first experience of bipolar disorder in high school, when she alternated between mania and an obsession with death and decay. Styron seems to present his illness in a more detached way, while Plath in particular invites the reader into her illness with phrases such as "I felt very still and very empty, the way the eye of a tornado must feel." Her prose is more immediate and more gripping. 
In addition, the women, Redfield Jamison and Plath, experience sexism that worsens their mental illness. Redfield Jamison, for example, is taken to task for refusing to curtsey when she is working as a candy striper, and it's clear that the expectations of being a girl in the military world in which she's raised add to her insecurity. Plath, for her part, is expected to live in New York as an experienced young woman, while she is innocent and unable to understand some of the ways the young women around her act with men. Styron's gender seems not to affect his mental illness in the same way in which gender affects the psychiatric experiences of the female writers.