"that provincial self-important twerp"

I just had to laugh when I read your well-observed remark!

I think you're right: Emma and Jane are very close to one another in importance. Emma, because of birth and fortune, and Jane, because of her accomplishments and experiences. Conversely, they both lack something. I always wonder that they should not be friends. Everything tends toward it, and yet, nothing happens on either side.

To me, Emma is jealous of Jane. She knows her own shortcomings when it comes to accomplishments and it distresses her to see them realized so well in Jane, whose background should not have prepared her to reach so high (according to Emma's rather stratified view of the world.) Add to this Miss Bates' constant praise and Highbury's general admiration of Jane, Frank's unscrupulous comments aimed at casting doubt on Jane's motivations, Jane's reserve (to be justified later), and you have a recipe for Emma the annoyed and catty (though with elegance... :-D )

Not the nicer side of Emma... She is still acting childishly at this point.

As for Jane, I think befriending Emma is not a priority for her (in any case, Emma, due to her position in society, should be the one who initiates the friendship, which she doesn't. Though it might bring her solace in her isolated situation, Jane is not about to ask for it. She seems a little proud in this respect.)

Jane is playing very close to the vest at this point in time. She's very guarded, which gives nothing for Emma to hold on to: now, that has to be very grating for gossipy!Emma. :-) I also think that, intuitively, Jane knows she and Emma can't really be friends. The similitude of their respective importance (as explained above) breeds an untold rivalry--mostly instigated by Emma--that Jane, being very sensible, must have sensed. But it's not something she can do much about.