Gender plays a key role in how Macbeth and Lady Macbeth deal differently with fear and guilt.
Lady Macbeth knows from the start that her internalized female gender norms will be an impediment to her ambitions for herself and her husband. She knows she has to repress every shred of what she considers female weakness and compassion and to present as more masculine than a man for the plot to murder Duncan to succeed. That is why she calls on the spirits to "unsex" her and
Come to my woman's breasts, / And take my milk for gall.
She specifically locates her gender as an obstacle, associating it with a part of her body—her breasts—used to differentiate women from men. She consciously works to eradicate everything her culture identifies as making a woman "naturally" more kind and loving. She realizes that she needs to do this to compensate for her husband, in her opinion, being too full of the "milk of human kindness."
Macbeth can think more rationally about the murder and almost stops himself because, somewhat secure in his masculinity, he can allow himself to contemplate and examine the inhumanity of what they are proposing to do. Lady Macbeth, so insecure about her "female" weakness, can't allow herself that luxury.
Not surprisingly, Lady Macbeth's deep repression ("keeping it inside") of her feelings emerges as the "return of the repressed" through her dreams and sleepwalking as she tries to deal with her guilt through obsessively washing the imaginary blood off her hands. This eventually leads to her suicide. In an opposite way, Macbeth's ability to "project it outside" leads to him severing ties with his humane emotions and becoming dead inside to guilt but also to the capacity to experience joy or other positive feelings.