To add to the excellent answer given above, both characters are involved in what are typically viewed as compassionate, people-oriented professions. Jason is a doctor, but his primary interest is not the patient but the field of research itself. He has his "own ideas" as to how to solve the cancer puzzle, a puzzle that intrigues him so much that he is insensitive to the emotional state of his patient Vivian. Vivian, as a professor of the poetry of John Donne, is very similar to Jason in this regard. As Susie comments, poetry is seemingly emotional and intuitive, but not the way Vivian Bearing taught it. Like Jason, her heart was in the research aspect of Donne's poetry, in solving the puzzle of the speaker's relationship with God, rather than in her students or even the emotional aspects of the poems she studied. She was a hard nosed professor who refused to have compassion for her students as individuals. And in her analysis of Donne's work, it seems that she might have missed the emotional impact that his eloquent words convey.
Both Vivian Bearing and Jason Posner are gifted, talented, and highly intelligent individuals, very capable in their chosen endeavors. At the play's end, we come to admire Vivian's toughness and strength. She never indulges in self pity and prides herself on learning the cancer vocabulary. She realizes the choices she has made in her career, and accepts the consequences. We are not as certain of Jason. He made a huge mistake in not recognizing the fact that Vivian was No Code and in trying to revive her "for research." We don't know how he will fare in the future, and we do not have the same admiration for him at the play's end.
Dr. Vivian Bearing and Dr. Jason Posner exhibit similar character traits in Wit. Before Vivian is diagnosed with cancer, she is a hard-nosed, strict professor who only truly believes in the value of her work. This is evident when she refuses to give an extension to a student whose grandparent has passed away. She believes in the rigidity of deadlines and in what she sees as the integrity of education.
Similarly, Jason is totally engrossed in his work with cancer patients and views Vivian as simply a subject that is available for him to study. He asks her blanket, routine questions in the manner that his mentor has taught him and he fails to see any human element to his work. His connection to Vivian is purely clinical in the same way that Vivian's connection to her students had been distant.
The similarity in their personalities is important in the play because Vivian begins to realize that she has been cold like Jason and their interaction provides Vivian with a platform for re-evaluating her own character.