Jane Eyre is a resilient woman, of higher moral calibre than Becky Sharp, but her happiness, and her psychological “completion”, seem to depend on her securing the love and companionship of another, Mr Rochester. All her battles from the orphanage onwards, with whatever doughty and feminist intelligence they are fought, are presented as leading to this one end.
I haven't read Vanity Fair, so I can't comment on Becky Sharp, but that's not how I remember Jane Eyre. As Laura Miller points out at Salon, the book describes "not Jane's quest for love but her assertion of her autonomy in a world that regards her as entitled to none."
In this respect, I would point out that Jane Eyre also has an autonomy edge relative to Elizabeth Bennett in Pride and Prejudice. When confronted by Lady Catherine de Bourgh about her suitability for Mr Darcy, Elizabeth's response refers to family identity--"He is a gentleman, and I am a gentleman's daughter." When similarly confronted Jane asserts herself based on her own character and actions.
Seriously, though, who are these people? The Telegraph also has an article today entitled: "Why I no longer worship at the altar of Robert Burns."