I posted the first week that I thought Emma was a moderate sized fish in a big pond. She leads an insular life in a small village, & her associations are even more contracted by her interpretation of her position in society which limits her contact to the six or seven people of appropriate standing almost all of whom have nothing but compliments for her.
Some folks have suggested that she may get to visit her sister & her family in London & I don't think there is enough evidence in the text to either support or deny that. However I would propose that these junkets to the big city are relatively infrequent & that Emma is rarely subjected to contact with fish her own size, let alone bigger ones.
Jane, on the other hand, due to her education by the Campbells has been swimming with the sharks for twelve years.
"Such was Jane Fairfax's history. She had fallen into good hands, known nothing but kindness from the Campbells, and been given an excellent education. Living constantly with right-minded and well-informed people, her heart and understanding had received every advantage of discipline and culture; and Col. Campbell's residence being in London, every lighter talent had been done full justice to, by the attendance of first-rate masters. Her disposition and abilities were equally worthy of all that friendship could do;" (Chapter 20)
It is likely that Jane has been acquainted with quite a few gentlemen's daughters with fortunes of thirty thousand pounds--(perhaps some even more), who had better educations, were more accomplished & better informed than Emma. Jane is beloved of the Campbells, the close friend of their daughter and is the darling of her grandmother & aunt. She has even been to "watering places."
Emma supposes that noticing Jane would be a great favor to Jane. What does Jane suppose? Jane cannot be unaware that in everything but birth & fortune (& future) she is Emma's superior. She must notice Emma's snobbery & its dependence on her lack of experience of other society. What does Emma have to offer Jane? Jane has family, friends, intellect & skills. In a closer association Emma would be the gainer given Jane's superior education.
Jane may also be aware of the impudence of Emma's questions about Mr. Dixon & Frank Churchill.
Do we think Jane is pining for increased contact with Emma, or might she be just as happy to minimize socializing with that provincial self-important twerp?