Both of these women love their brothers, and both mourn their loss. However, Olivia retreats from life and turns away from love, denying Orsino's proposal of marriage.
Viola, by contrast, takes action to make her life better. In a way you might say that Viola can't be a woman now either, because she disguises herself as a man, but as a man, she falls in love with Orsino, and takes action that eventually leads to her union with Orsino and Olivia's with Viola's brother Sebastian.
Their responses are similar in some respects, but different in the degree of activity, and in their openness to life and love.