Emma seems to have some similarities to the people around her, in both good and bad traits. She and Mr. Woodhouse like people to visit them on their own terms, and will see, nor hear, nor speak any ill of each other.

She and Mrs. Weston both like the idea of matchmaking the people they like with one another, and manage good manners even when faced with irritating people. (Emma's propriety has slipped I know, but one can hardly say her offenses outnumber her forbearances.)

She and Mr. Knightley both think they can guess who will be good together and who will not, and hold action intended to injure in utter contempt.

She and Harriet both MEAN to educate themselves, but find it easier not to, and socialize instead.

Emma and Mrs. Elton both like to consider themselves as the social leaders, the charity-granters, the one who knows how to do things right.

Emma and Mr. Elton tend to pick a desired outcome and see all clues that support that and none that disprove it. (I might be being unfair - I think this is a human trait, although for some people it is the opposite -- they foresee gloom and doom, and neglect any aspect of a situation that proffers hope.)

Emma and Miss Bates allow their tongues to run away with them on occasion, and both dote on their families, never seeing how they accommodate their family's failings, since they do it so often it is second nature to them now.

Frank Churchill and Emma love a joke on others, setting themselves up as being 'in on' some secret news, and enjoying simple socializing chat.