Charlotte Lucas and Elizabeth Bennet are best friends, showing how opposites can mesh and build happy friendships until a decisive turning point comes along, such as Collins' marriage proposal(s). In a foreshadowing of Austen's other greatest work, Sense and Senibility, Charlotte represents sense (making sound judgements and decisions) while Elizabeth represents sensibility (making emotion-driven judgements and decisions). While Charlotte is willing and able to see things in their unembellished reality, Elizabeth idealizes and either trivializes (e.g., Darcy) or magnifies (e.g., Wickham) things that she sees.
With these characteristics in mind consider how Charlotte unflinchingly meets reality with action by being the chief cook for the Lucas family since the reality is that though Sir Lucas has a title and has been presented at court he hasn't got the income to support a lifestyle in tune with his title. Consider how this same characteristic leads Charlotte to apply soundness to her evaluation of Collins' "rebound" proposal; to her decision to accept his proposal; and to her actions in cleverly establishing a pleasant and happy life for herself:
Mr. Collins invited them to take a stroll in the garden, which was large and well laid out, and to the cultivation of which he attended himself. To work in his garden was one of his most respectable pleasures; and Elizabeth admired the command of countenance with which Charlotte talked of the healthfulness of the excercise, and owned she encouraged it as much as possible.
With Elizabeth's contrasting characteristics in mind, consider how Elizabeth overlooks her father's disrespectful and neglectful parenting (which she acknowledges at the end of the story) while learning to ironically make fun of people's foibles and weaknesses, including her own. This trait causes her to misjudge individuals whom she then either accepts or rejects based not upon a sound evaluation but upon her emotional reaction to them. Consider now how this characteristic might have led her into a marriage with the fortune hunter, Wickham, and how this same characteristic caused her to misjudge Darcy thus causing herself much unhappiness (and him untempered insult).
While Charlotte and Elizabeth are equally intelligent, equally good natured and pleasant, equally of high birth (gentlemen's daughters are eligible marriage partners for all ranks of the upper class, including nobility), Charlotte sees the world through perceptions that seek and cause her to respond to reality, while Elizabeth sees the world through perceptions that laugh at foibles and cause her to respond according to how her emotions are stirred by these foibles.
In the episode of Pride and Prejudice by Jane Austen when Darcy refuses to dance with Elizabeth at the ball, the narrator says:
Elizabeth.. told the story, however, with great spirit among her friends; for she had a lively, playful disposition, which delighted in anything ridiculous.
In contrast with Elizabeth Bennett, Charlotte Lucas is very serious and not particularly clever. She is, however, immensely practical. Rather than turning down Mr. Collins offer of marriage, she accepts it because of economic necessity. While in the novel, we sympathize with Elizabeth, and her refusal to marry Collins, in reality, Elizabeth's refusing a perfectly acceptable marriage offer would be like someone now turning down a steady, if boring, job because they believed they might win the lottery. In this way, clever and interesting as she is, Elizabeth is also impractical and unrealistic, weighing her happiness over family loyalty.