In both of these pairs, there is a secondary individual and a primary one. Bingley and Jane are secondary while Darcy and Elizabeth are primary. The interesting paradox (seeming contradiction between truth and what is) is that the two secondary individuals teach the two primary ones lessons and are proven correct in situations where the primaries are proven incorrect. The foundation of each of these pairs is a deep mutual bond of love, esteem, admiration and friendship.
While Bingley and Jane are, for the most part, followers of Darcy and Elizabeth, respectively, they are also the voices of reason while Darcy and Elizabeth are the voices of emotional reaction. This may seem an odd statement to make about Darcy, but his censure of Elizabeth at the Meryton ball was based entirely on feelings: he didn't feel comfortable with strangers; he didn't feel there was status in dancing with someone whose beauty was of secondary lustre; he didn't feel inclined to talk to anyone not in his own party (Bingley, Mrs. Hurst, Miss Bingley, Mr. Hurst). In contrast, Bingley and Jane represent reason throughout when they urge their friends to be more tolerant and open (Bingley-Darcy) or to be more accepting and generous (Jane-Elizabeth).
Between him and Darcy there was a very steady friendship, in spite of great opposition of character. Bingley was endeared to Darcy by the easiness, openness, and ductility of his temper, though no disposition could offer a greater contrast to his own,
In the end, Bingley's willingness to disregard Jane's family and connections and accept Jane for herself proves correct while Darcy's impulse to withdraw from the Bennet family and connections proves incorrect. In the end, Jane's willingness to have generous and accepting opinions of acquaintances proves correct (except as regards Wickham and the Bingley ladies who were represented as being bad beyond her previous experience), while Elizabeth's impulse for instant prideful and prejudicial likes or dislikes proves incorrect.
[Elizabeth] "Pleased with the preference of one, and offended by the neglect of the other, on the very beginning of our acquaintance, I have courted prepossession and ignorance, and driven reason away, where either were concerned. Till this moment I never knew myself."
Attitudes towards marriage in Pride and Prejudice are dictated by ones social standing. Bingley treats marriage with an amused frivolity, and wants to marry whomever he wants and attend balls, and enjoy life and the money that he is endowed with. He is clearly a character with little to no responsibilities, and a kind demeanor and so can pursue love rather than social connections. His social standing is extremely high, especially in the little villiage he finds himself in. Thus, he can treat marriage with less seriousness than say, a character like Mrs. Bennett. Now, Mrs. Bennett is not only lower class in society and not very well endowed in assets, she has 5 daughters to marry off. In this time in England, a daughter is the biggest possible burden: they need dowries, they must be talented enough to be an asset to the families they marry into, and marriage is a serious business for these women. Mrs. Bennett must marry off her five daughters into fine, upstanding families, in a way that does not compromise their family. Mrs. Bennett cannot afford to think about love or any such frivolities in the slightest, indeed, she even asserts that "love has nothing to do with marriage." The rest of the characters fit in between, with Mr. Darcy of course being a character whose pride blocks him from marriage, even as his wealth is abounding. However, each characters stance on marriage is a direct correlation with their social standing.
Another fact obviously comes from the different genders. Mr. Bennett is utterly contemptous of marriage, simply for the frivolity it provokes in his wife and daughters.