Does emotion or logic triumph in Sense and Sensibility?

It's easy to see Sense and Sensibility as a story in which logic ("sense," Elinor) is pitted against emotion ("sensibility," Marianne) but I think that is a misreading of the book. I think Austen's point is that both qualities are necessary for happiness and that both Elinor and Marianne suffer as a result of favoring one over the other.

In Marianne's case, her relationship with Willoughby is an example of an excess of sensibility. Marianne truly believes that she and Willoughby share a deep understanding that they discover by way of their mutual appreciation of art and literature. In Chapter 9, Austen writes of the pair:

Their taste was strikingly alike. The same books, the same passages were idolized by each—or if any difference appeared, any objection arose, it lasted no longer than till the force of her arguments and the brightness of her eyes could be displayed. He acquiesced in all her decisions, caught all her enthusiasm; and long before his visit concluded, they conversed with the familiarity of a long-established acquaintance.

It is an open question how much Willoughby might actually feel for Marianne; Austen's sly comment about how any disagreement was settled "by the brightness of her eyes" suggests that Marianne might be wrong about his enthusiasm for literature. Marianne and Willoughby seem to have a lot in common, but (we find) Marianne is wrong about him: Willoughby's subsequent actions—his cutting Marianne at the ball, and eventual marriage, and especially his desperate visit to the sick Marianne in Chapter 44—show that passion, however heartfelt, is not a firm basis for a relationship.

Elinor is similarly deceived by Edward. Unlike Marianne, who perhaps is too open with Willoughby, Elinor's struggle with Edward is to find a safe space in which they can talk. This "delicacy"—the guarded way of speaking that Marianne cannot stand—has its own costs. Edward also has a secret: even though he is attracted to Elinor (and pursuing her in his way), he actually is engaged to Lucy Steele. And also like Willoughby, Edward seems unaware of how his behavior affects others. In Chapter 49, Elinor tells him his behaviour was wrong, and he replies:

“I was simple enough to think, that because my FAITH was plighted to another, there could be no danger in my being with you; and that the consciousness of my engagement was to keep my heart as safe and sacred as my honour. I felt that I admired you, but I told myself it was only friendship; and till I began to make comparisons between yourself and Lucy, I did not know how far I was got. After that, I suppose, I WAS wrong in remaining so much in Sussex, and the arguments with which I reconciled myself to the expediency of it, were no better than these:—The danger is my own; I am doing no injury to anybody but myself."

Elinor smiled, and shook her head.

In fact, Edward caused a great deal of suffering. Elinor's mortification on finding out about Edward's engagement, and her determination to keep Lucy's secret despite the personal emotional cost, cost her dearly.

It can be argued that Marianne's marriage to Col Brandon shows that Austen values sense over sensibility, but to me all the characters are only able to fully connect with each other when they embrace both sense and sensibility: Marianne must learn the hard way about her openness with Willoughby, and Elinor is only happy when she can at long last unburden her heart to Edward.