"First, they have both had disappointment in proposed marriages but they are of very unequal value."

I think you've hit on the right track with the jealousy angle, but you need to go a step further. Elizabeth was never even engaged. She is beginning to panic because she is not yet married, her father is perfectly oblivious to her panic (not that he could do more for her than he aleady has) and I think Elizabeth begins to resent that Anne ever even had a single proposal of marraige let alone two. Anne's unmarried state is entirely her own choice, Elizabeth has been forced into it, by virtue of the fact that no one has wanted her. That is why Elizabeth always stresses that no one wants Anne. It is really her own worst fear. Some people bring themselves up by the low means of bringing others down.

Elizabeth is actually in a precarious spot though she doesn't realize it. She is mistress of her father's house, so like Emma, she has passed her twenties with a lacsidaisical attitude that she is in no hurry to marry, but unlike Emma, she will not inherit and she has no substantial fortune of her own to catch the sort of man she wants. She is also at the very tale end of what would be considered a marraigable age and Emma was only 21. Add to that the real possiblity that Sir Walter could remarry and have another child, Elizabeth could easily be in the position of being entirely dependent. Time is running out and that desperation makes her snippy.

To make matters worse she has a deep sense of entitlement: she is owed a home of her own, with a husband who is well-connected and rich. Any gentleman she meets in London likely to be within her reach is probably not going to be good enough for her.

I agree that her actions toward Anne also have a fair amount of pure maliciousness in them. This is not something that either Sir Walter or Mary have. They are selfish, petty and vain, but I do not think they deliberately mean to be cruel. Elizabeth does. Why? Well, it's pure bully psychology. She feels powerless. She is in a tough spot, and she makes her self feel more powerful by picking on someone weaker. She is mean to Anne because she can be.