The difference between Jane and Emma is that, whilst Mr W likes to show off Emma's needlework, pictures, etc, Emma knows that Jane's are actually better. She is, therefore, irritated by Mrs and Miss Bates showing off Jane's work. She is jealous, too, that Jane is as accomplished as she wishes to be - probably because she takes the time to practice, whereas Emma would like to be good 'naturally'!

Jane has no need of Emma's patronage as Harriet does. She has enough beauty, sense, education and accomplishments of her own. Emma, therefore, has nothing to offer Jane other than friendship. She feels that her previous efforts have been spurned by what she sees as Jane's coldness.