What are the points of similarity and difference in "Wuthering Heights" and "Jane Eyre"? How are the Brontë sisters similar and different in their respective novels and writing styles?
That's a huge question. The conventional wisdom is that Wuthering Heights is a novel of grand passions, filled with Gothic touches, while Jane Eyre is more buttoned down, more concerned with propriety and Christian values. While this may be outwardly true, I think both novels have quite a bit in common. Here are a few elements:
Rochester and Heathcliff: Both novels feature strong male characters who share certain characteristics of the Byronic hero -- a powerful, solitary figure with a mysterious secret, reclusive, rebellious, dangerously attractive.
Marriage: Both books focus on the problem of marriage, and, in particular, wrong marriages: Catherine's marriage to Linton is (for Heathcliff) an unthinkable betrayal; Rochester's marriage to Bertha was (according to Rochester) the result of subterfuge and somehow unnatural. Heathcliff's marriage to Isabella is another perversion, a marriage for revenge, not love; Jane Eyre narrowly escapes a wrong marriage herself -- had she married St John, it would have been out of religious duty, not love. Only at the end of Jane Eyre, when Jane finally marries Rochester, do we see a marriage that is mutually fulfilling.
Class: Both books deal with the question of class and identity. Heathcliff is an orphan who is brought home by Mr. Earnshaw as a surprise addition to the family; no one knows who he is or where he comes from -- in effect he has no social identity at all. Jane Eyre, as governess, has a clear place in the social order -- quite a low one. When Rochester chooses to marry her he is upsetting the social order, in effect publicly valuing Jane in spite of her low status. Both Heathcliff and Jane, from a class point of view, are outsiders, or interlopers. While these two characters respond to their situations very differently, who they are as people is not determined solely by class. Both books are about the struggles of powerful individuals.
It is interesting to consider with the Bronte sisters how the novels reflect the lives of their authors. By all accounts, Emily Bronte was much more Romantic (with a capital "R") than her sister, and also much more focussed on the Yorkshire Moors, where the Brontes grew up. She was desperately homesick whenever she left her beloved Moors, and this certainly gives rise to one of the differences between the novels. Wuthering Heights is very narrow in its geographical setting - all the action happens in a very small patch of the moors, and when characters leave, it is as if they have fallen off the edge of the world - they disappear from the action until they return. This is in contrast with Jane Eyre, where the protagonist definitely moves around and the action occurs in 5 different locations.