You are right in identifying that this novel, like Pride and Prejudice, relates the two central protagonists to the states indicates in the title. The "sense" refers to Elinor, who is shown to suffer through similar trials to her sister. However, significantly, Elinor never expresses her emotions completely and does not let her own personal misfortunes and disappointments impact how she reacts towards others. She is above all a very stoical individual, who, even when she is suffering greatly after finding out about Edward's engagement to Lucy, continues to act as a friend to Lucy in spite of her heartbreak. She shows how sense rules her emotions.
By contrast Marianne represents "sensibility." Let us not forget how Marianne acts towards situations. She jumps in completely, expressing all of her emotions to Willoughby and criticising Elinor for her reserve. She displays freedom in terms of her passions and emotions, and this is depicted by Austen as being selfish compared to the stoic resolve of her sister. The harsh realities of life will definitely make living unbearable for somebody who is ruled by sensibility, as Marianne's subsequent response to Willoughby's abandonment of her shows. Marianne takes to her bed and is unable to function in everyday society, whereas Elinor continues to fulfil the various social obligations of day-to-day life. The strength of sense vs. sensibility is shown by Marianne's marriage to Colonel Brandon, which is based on common sense and not on passionate emotions.