The characters of Caroline Bingley and Elizabeth Bennet in the novella Pride and Prejudice are hard to compare and easier to contrast.
Caroline Bingley is unmarried and rich, but does not have any aristocratic background. For this reason, she is very subservient to Mr. Darcy and basically woos him to get his attention. She seems to be unsure of herself, which is manifested in the way that she tries not to speak her mind too much, and is agreeable to everything that Darcy says and does. Her ultimate goal is to become the future Mr. Darcy. She clearly sees that Elizabeth is her competition and, for this reason, she talks about her negatively.
Elizabeth was also unmarried. She was not rich, nor did she have a dowry substantial enough to propose herself as a potential wife to a man as rich as Darcy. She was not an aristocrat either. Yet, in contrast to Caroline, Elizabeth did not care at all about rank, position, nor money. All she wanted was to truly love someone. She was an independent thinker, spoke her mind, and did not make distinctions when it was time to say what needed to be said.
If the two women were to be compared, the only things that they had in common were that they were both of a "marriageable" age, that they were not aristocrats, and that they got along well with Jane (until Caroline betrayed her). Other than that, the women contrast almost completely.