young women, are likely making their own decisions for the first time. Olivia's choice is to withdraw from the world, ostensibly for seven years. In doing so, she ignores the natural call of youth, which typically draws—at least in Shakespeare—the person toward love. Viola withdraws into her male identity, seemingly denying her feminine youth as well, becoming something of a counterfeitSebastian.

Viola immediately decides to improvise a life in Orsino's court. She is open to falling in love with him and is able to connect to all the various characters in Illyria. She accepts the madness of love and human existence but pushes forward. When she is forced to woo Olivia for Orsino, she does so as best she can, taking the wry perspective that she would rather be the wife of the man for whom see is seeking Olivia's hand. Similarly, Olivia, after Viola's "willow cabin" speech, falls in love, breaking her vows to not entertain others, especially regarding marriage proposals. She makes a fool of herself and, like Viola, admits that she is subject to folly. She persists nonetheless.

In these important respects, the women are quite similar. An important difference lies in Viola's role as a catalyst in the stagnant Illyrian world. Olivia likely would not have grown or abandoned her grief were it not for Viola's accidental presence in this world. She would likely have fulfilled her vows and become more entrenched in her absolutism, much as the rest of her household is entrenched in theirs: Malvolio (strict puritanical order), Toby (excessiveness). Viola proves a change agent for all.

Both Olivia and Viola are women of high social status who have recently lost (or believe they have lost) their brothers. Though they are similar in background, their responses to the deaths of their loved ones are quite different. While Olivia's grief has forced her to close up the doors of her home and admit no suitors, Viola's grief and sudden change in circumstances force her to disguise herself as a man and go into service for Count Orsino, pretending to be both a different gender and a different class.

Another similarity between the women is that both Olivia and Viola's mourning periods are interrupted by an unexpected infatuation. Olivia is snapped out of mourning by the onset of her love for Cesario, while Viola's grief is given almost no stage time before she begins pining for Orsino.

Finally, though Olivia initially holds a cynical view of love, she is almost immediately swayed by Viola/Cesario's overtures of love, proving that both women are romantics at heart.

Both Viola and Olivia are women who belong to the aristocracies of their respective communities. They are "gently bred" and educated in womanly arts rather than in such masculine skills as swordplay and classical languages. Both, at the time of the play, are young, single, and attractive. Both have or had beloved brothers, but while Olivia's brother is actually dead, Viola's has merely been separated from her by a storm, although it takes them some time (and many comic plot twists) to be reunited. 

That being said, the two young women differ greatly in character. Olivia has become distraught over the death of her brother, while in adversity Viola displays great strength of character and intelligence. Olivia seems more conventional than Viola and also more emotionally melodramatic, while Viola has greater self-control and sense of purpose. Despite this, Olivia at times displays flashes of insight, as when she dismisses praise of her appearance with an inventory of her beauties: 

Item, two lips, indifferent red; item, two grey eyes, with lids to them; item, one neck, one chin, and so forth.

This suggests that, as a wealthy young woman, Olivia has learned to take a somewhat cynical view of her suitors, seeing that they are interested only her her appearance or wealth, and her being attracted to Viola's kindness and intelligence actually does suggest good judgment.

Viola and Olivia are both gentlewomen raised to self-esteem, manners, breeding, wealth and luxury (Olivia more so) who both recognize and accept the role of Fate in their lives. This is where their character descriptions part company. Olivia's overriding trait is emotional foolishness. Her brother has recently died after a good religious life because Feste declares him to be in "heaven." Olivia's response of mourning is to mourn for seven years with her face under a veil while refusing all declarations of love and weeping daily. Viola, in contrast, has lost her brother and takes the encouragement offered by the Captain to hope for the best results for her brother. She accordingly develops a plan for coping with life without her brother and pursues it, even though it is certainly a plan for life that she never would have thought of prior to her loss. Both women fall in love at first sight, but Viola falls only once whereas Olivia falls once and switches once when she marries Sebastian. Speaking of which, Viola seems to have made the worse choice in her object of affection while Olivia seems to have made the better choice: Orsino is emotionally volatile and changeable whereas Sebastian is Viola's twin, which suggests her twin in character traits also.

Shakespeare's Twelfth Night is a romantic comedy concerning the loves and adventures of two pairs of lovers, Sebastian and Olivia and Orsino and Viola. All of the protagonists are members of the upper classes and all are initially thwarted or misguided in their romantic endeavors, but eventually, after many plot twists, mistaken identities, and other entertaining episodes, both pairs of lovers end up happily marrying the right people.

Viola and Olivia are similar in that they are young, attractive women of the upper classes who appear to have recently suffered the loss of their brothers. Both are in love with people who seem unlikely to requite their love due to issues of gender. Both are concerned with the inner nature of their suitors rather than just wealth and power. 

The main difference is that Olivia is portrayed as living at home, enjoying wealth and position under her own identity, while Viola has been shipwrecked and is disguised as a boy and employed as a page. Olivia's brother is actually dead, but Sebastian, Viola's twin brother, lives, and is frequently mistaken for Viola. Viola is in love with Orsino, but Orsino does not know she is a woman. It is only when her true identity is revealed that Viola can move from the position of page to wife, as Orsino sums up in the following passage:

Your master quits you; and for your service done him,

So much against the mettle of your sex, ...

And since you call'd me master for so long,

Here is my hand: you shall from this time be

Your master's mistress.

Olivia's attraction to Viola as a man is resolved when she ends up marrying Sebastian, Viola's male twin, and thus the true version of what Viola was merely pretending to be. 

Both young women approach life from entirely different directions.

Olivia seemed to enjoy her self denial.  She is self indulgent.  One only has to look at Feste in Act I, scene 5.  He proved that she was acting foolishly.  When he asked her why she was in mourning, she replied it was for her brother's death to which Feste responsed that his soul must then be in hell.  Olivia answered that it was in heaven.  Feste replied that it was foolish to mourn someone whose soul is in heaven.

When she "fell in love" with the disguised Viola, it was more the novelty of new face.  Her marriage to Sebastian was based on a misconception.  She really didn't know him.

Viola, on the other hand, embraced life and, despite the fact that she thought Sebastin had died in the shipwreck, she decided to disguise herself as a young men and dress like her brother in order to pull it off.

She also recognized that Orsino is in love with the idea of being  in love and in Act II, scene 4, she taught him about love.  Their marriage was much more realistic since Orsino was already, in a sense, in love with her as Cesario.

Both women are educated and come from noble families but each have different ideas about life and love.  

Orsinio, the Duke of Illyria, is an intense, emotional, and passionate man who is in love with the idea of love. A statement he makes early in the play characterizes him:

If music be the food of love, play on!

Orsinio loves sensual pleasures and is often overly emotional, sentimental, and bombastic—tending to use inflated or exaggerated language.

Viola, in contrast, is self-controlled and dignified. As a person shipwrecked in Illyria, she has to survive by her wits and does so by pretending to be a man. Witty and intelligent, she has to be careful about everything she does so as to not slip up. Despite her ruse, however, Viola's manners and personality are attractive to the duke.

Orsinio, as a duke, can indulge his emotions and temper; he expects others to cater to him and overlook his excesses because of his position of power. Viola, because of her relative powerlessness, must keep her emotions under control and be attuned to the moods of those who are higher ranking than her.

What they share, however, is love. Viola is in love with Orsinio, but because she is disguised as a man, can't show it, while Orsinio, though he doesn't know it, is in love with Viola. Viola's love is much more restrained and silent than Orsinio's sentimental outbursts, but it is still love. She explains (while pretending to speak of someone else):

She never told her love,But let concealment like a worm i' th' budFeed on her damask cheek. She pined in thought,And with a green and yellow melancholyShe sat like Patience on a monument,Smiling at grief. Was not this love indeed?