I think this common thread does not appear in Mansfield Park -- where, instead of opposites attract, the heroine Fanny and the hero Edmund are very similar to each other. But serious Edmund had previously believed that serious and lively characters could complement each other, and had been earlier attracted to a lively woman -- until he found out that she had "faults of principle".

JA wrote Emma immediately after MP. MP had unhappy outcomes for some characters, while Emma had happy outcomes for everyone. I often think that the characters of the two books may be compared in this way --

1. Emma is the heiress to 30,000 pounds and Mary Crawford had 20,000 pounds, they both had lively dispositions, Emma had faults, but they were not "faults of principle", because she had been taught good principles by Miss Taylor, even though she was over-indulged, while Mary C had been brought up by her aunt, the embittered wife of an unfaithful husband to be worldly and cynical.

2. Mr Knightley and Edmund were both well-principled with serious dispositions, but Edmund was younger and less mature. Mr Knightley had guided Emma, who often appeared to resist him, while Edmund had guided Fanny who had always adored him.

3. Frank Churchill and Henry Crawford were both thoughtless and inconsiderate -- but Frank Churchill appeared more boyish than Henry, though I think Mr Knighley's words in chap 49 on Frank could also apply to Henry if he had won Fanny --
"I have never had a high opinion of Frank Churchill [Henry Crawford]. I can suppose, however, that I may have under-rated him ... With such a woman [as Jane Fairfax/Fanny Price] he has a chance ... and for her sake, whose happiness will be involved in his good character and conduct, I shall certainly wish him well."

4. Jane Fairfax and Fanny Price -- Jane was raised by her friends the Campbells, who treated her like another daughter and gave her the advantages of a good education and good society, but were unable to provide her with a dowry. Fanny was raised by her relatives at Mansfield, where she was obviously inferior to her cousins, but her uncle was going to provide her with "the provision of a gentlewoman".

An Emma-Knightley and Jane-Churchill pairings seem almost to reflect what might have been in an Edmund-Mary and Fanny-Henry pairings -- if Edmund had been more mature, if Mary had a serious spirit as well to correct her faults, if Fanny had returned Henry's regard, and if Henry had been more constant. On the other hand, a Jane-Knigtley and Emma-Churchill pairings would have been in a way almost a repeat of MP pairing -- with Jane-Knightley reflecting Fanny-Edmund, and Emma-Churchill -- well they are not likely to improve each other, and if Henry and Mary were not brother and sister, they might have paired off with each other.