This is such a great question! After having read the previous two answers, I think I can add a bit.
It's important to note that Vivian is not just a hard-nosed, cold professor, she was specifically Jason's professor. Jason, in part, is who he is BECAUSE of Vivian. She taught him.
Jason sat in Vivian Bearing's class and watched her eviscerate her students, something she admits made her feel powerful. She reveled in the puzzle of John Donne's sonnets, just as Jason revels in the "awesome" puzzle of cancer. She had no tolerance for ignorance in her classroom, admittedly the toughest, and her standards were unwittingly (no pun intended) passed on to Jason, who likewise scoffs at those who are less dedicated to research than he is. After Vivian is under ameliorative care, he even admits to Susie that the puzzles of Donne's poetry and the way Bearing taught them were "great training for lab research."
During their respective work, neither of them sees the value of the "part with human beings." Though they both, as has been stated, are in fields of human service, neither of them understands the importance of humanity. At least not until it seems too late.
Vivian comes to realize that her example has left her with a "young doctor" who "like the senior scholar, prefers research to humanity." It is not until she needs a human touch that she regrets her own behavior.
Another response questioned whether Jason will change after his mistake of calling a code on Vivian's "No Code." I think he will. I think that both he and Vivian are scholars, and both capable of learning. Susie rebukes Jason for calling code on his DNR patient, and he retorts that "she's RESEARCH." But when he realizes his error, and he does, he says, "Oh God" not once, but three times with intervals between. He is confronting his careless disregard in much the same way as his teacher had to face herself and God, and he saw his error too late for Vivian, but not too late for life. Vivian Bearing's last act as Jason's humanities teacher was to teach Jason humanity.
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.