What are the similarities between Orsino and Malvolio in Twelfth Night?

Firstly, Orsino and Malviolio are linked in their mutual pursuit of Olivia's love. While their social statuses are very different, they both exhibit pride, self-importance, and inconstancy of character.

Beginning with pride and self-importance, Orsinio is a Duke. He is wealthy, well-situated in society, and a bit full of himself. In the opening scene of the play, we see Orsino respond to the news that Olivia will not see him because she is in mourning for her dead brother. Rather than being sympathetic to Olivia's suffering, Orsinio makes this about himself.

O, she that hath a heart of that fine frame
To pay this debt of love but to a brother,
How will she love, when the rich golden shaft
Hath kill'd the flock of all affections else
That live in her;

Orsino's thought is not to Olivia's grief, but to how much she would grieve over his death if her grief is this great over a loss as insignificant as that of a brother. Furthermore, despite his apparent love for Olivia, he considers his own understanding and experience of love to be greater than that of any woman, as seen in his conversation with Viola (Cesario) in Act 2, scene 4.

Malvolio is aptly characterized for his sense of self importance by Maria in Act 2, scene 3.

The devil a puritan that he is, or any thing
constantly, but a time-pleaser; an affectioned ass,
that cons state without book and utters it by great
swarths: the best persuaded of himself, so
crammed, as he thinks, with excellencies, that it is
his grounds of faith that all that look on him love
him; and on that vice in him will my revenge find
notable cause to work.

Maria's opinion of Malvolio is shared by Toby, Andrew, Fabian, Feste, and even Olivia. It is because of Malvolio's self-importance that he is subject to the cruel pranks set upon him by Toby and company. We see in Malvolio's own demeanor and speech that he considers himself to be superior to the other characters in the play, including those of higher status than he, such as Toby and Andrew. Despite the fact that he is a steward, he does not even question the probability that Olivia could be in love with him. He thinks of himself that highly.

This pride connects to both characters' changeability. We have two men in love with the same woman, but as the play unfolds, we find that love to be inconstant or untrue. Orsino's affections shift from Olivia to Viola (though he is confused because he believes Viola is a boy) pretty easily. His love for Olivia is not substantial - he does not even go in person to speak to her. He sends other people and pines. Orsinio seems to be in love with the idea of being in love more than he is actually in love with Olivia.

Malvolio's love seems to be grounded in a desire for advancement more than in any actual romantic feeling. He never describes Olivia's beauty or his feelings toward her. All of his thoughts are focusing on achieving higher status. The best way to achieve this, in his mind, would be through a marriage to Olivia.