The title of the book itself could be construed as representing the main conflict. Elinor is the Dashwood sister with "sense" in the story, whereas Marianne is, for the most part, a slave to her sensibility, or emotions. As well as her undivided attention, Marianne gives Willoughby a lock of her hair. The bestowal of something so intimate symbolizes the giving of Marianne's heart to her new beau. In the long run, however, once Marianne comes to her senses, she will find a suitable husband for herself instead of lavishing her attentions on the likes of Mr. Willoughby.
There are also a number of metaphors in the book which pertain to the sense versus sensibility conflict. A metaphor can be defined as a person, place, thing, or event that stands both for itself and for something beyond itself. In the scene where Mr. Willoughby assists Marianne after her accident, he's out hunting, and he's introduced to us as carrying a gun, with two pointers playing around him. Metaphorically speaking, Willoughby is hunting Marianne; she is his quarry. And just as a hunt's quarry ends up being put through a lot of pain and suffering, so too does poor Marianne suffer emotionally from her ill-advised involvement with the frightful Willoughby. In this particular case, sensibility prevails over sense.