Duke Orsino's love for Olivia is really more of an obsession. As we learn in the very first scene, his obsession for her began at first sight. But not only is he obsessed with her, he is obsessed with the idea of being obsessed with her. He has experienced a great deal of pain due to her rejection of him, and instead of allowing himself to recover and move on, he allows himself to sink even deeper, becoming obsessed with his obsession. In addition, he does not have concrete reasons for being in love with her. He has never spoken with her as she is rejecting the company of all men since her bother's death. Instead, he is only in love with her beauty, thinking her so beautiful that she could purge the "air of pestilence," meaning heal the world around her (I.i.21). What's more, even her obsessive grief over her bother makes him believe that if she could love a brother so much, how much more would she love a man she was in love with, as we see in his lines:
O, she that hath a heat of that fine frame
To pay this dept of love but to a brother,
How will she love, when the rich golden shaft [Cupid's arrow]
Hath kill'd the flock of all affections else
That live in her. (35-39)
Hence, Orisno's thought that Olivia could love very deeply once in love makes him hold on to his hope of one day securing her, making him even more obsessed with his own obsession for her.
Viola, on the other hand, has not only spoken with Orsino whom she is in love with, she actually grew up hearing her father praise his character. We learn of Viola's prior knowledge of Duke Orsino in the second scene when she first arrives in Illyria. The sea captain who rescued her praises Orsino's character, saying he is just as noble in character, or "nature," as he is noble in title, as we see in the captain's lines, "A noble duke, in nature / As in name" (I.ii.25-26). Viola next says she had very frequently heard her father speak of him when her father was still alive, which was prior to Viola turning 13. Hence, if the duke is as noble a person as the captain describes, then we know that Viola grew up hearing her father comment on his nobleness as well. Thus, it is no surprise to learn that Viola has fallen in love with Orsino immediately after beginning to work for him. Plus, since Viola has fallen in love with his character, we know she is truly in love with the man, rather than just being in love with the idea of being in love with him or obsessed with him in the same way Orsino is obsessed with Olivia.