The contrast between the Derbeyfields and the Clares is rather stark though there is surprisingly one similarity between them. The similarity is that both John (Jack) Derbeyfield and Vicar Clare are men who are proud of their background and lineage. Jack didn't have much reason for his pride until Parson Tringham told him of the newly discovered connection to the ancient house of the Norman nobles, the d'Urbervilles, yet once that was known Jack's Derbeyfield pride of family matched Vicar Clare's.
"Sir John d'Urberville—that's who I am," continued the [reclining] man. "That is if knights were baronets—which they be. 'Tis recorded in history all about me."
The above points out the occupational contrast between the Derbeyfields and the Clares. Vicar Clare is a highly educated clergyman as are two of his sons. His third son, Angel, disappointed him by not following in the expectations of the family. Jack Derbeyfield is an undereducated "haggler" who sells eggs and bees in the small village of Marlott. His eldest daughter, Tess, has similarly disappointed him by not following in the family expectation by not securing the patronage of the new d'Urberville family and by coming home to have a baby without accepting an offer of marriage from the child's father.
"I have never really and truly loved you, and I think I never can." [Tess] added mournfully, "Perhaps, of all things, a lie on this thing would do the most good to me now; but I have honour enough left, little as 'tis, not to tell that lie."
In their deeper backgrounds, the Derbeyfields are descended of French Catholic nobility while the Clares are descended from English Puritan (Protestant) gentry and clergy. This makes the Derbeyfield ancestry of a higher rank than the Clare ancestry, though at the time of the story, the Clare's are higher in social rank. Another thing the families share in common is their willingness to be accepting, forgiving and loving, though Vicar Clare seems to have a few more limiting restrictions and qualifications attached to what he will accept, forgive and love.
The fathers of both families set the overall tones of what the families are like though Mrs. Derbeyfield has more influence in her family than Mrs. Clare seems to have in hers.