Although it would not seem like it at first, Magwitch and Miss Havisham actually share many similarities.
1. They both hate Compeyson, the second convict on the marsh in the book's opening. Miss Havisham has great reason to dislike him because he was in cohoots with her brother for the marriage scheme and is the one who leaves her at the altar. Likewise, Compeyson drags Magwitch down with him, betrays him, and eventually causes him to lose all his money.
2. Both characters are devastated by their lovers' despicable actions. Miss Havisham's fiance not only leaves her at the altar, but she discovers that he never loved her in the first place. This truth embitters Miss Havisham for much of her life. Magwitch's wife Molly (Jaggers' house servant with the scars on her wrist) kills someone Magwitch was supposedly involved with and causes their baby to disappear; so Magwitch goes his whole life thinking that his precious little girl is dead.
3. Magwitch and Miss Havisham are parents--of sorts--to Estella. Magwitch is her biological father and discovers on his death bed that his daughter lived and became a beautiful woman, and Miss Havisham raises Estella. She seems to love Estella in a strange way, but ultimately the manner in which she raised Estella does more harm than good. Thus, you can infer that Magwitch and Miss Havisham are responsible for hurting Estella, although neither did so intentionally.
4. Both are connected to Pip's mysterious benefactor. Pip assumes that Miss Havisham is his benefactress, while Magwitch actually is his benefactor.
5. In connection to number 4, Miss Havisham and Magwitch both choose children to "train" and develop. Miss Havisham trains Estella to be immune to men and uses her to exact her revenge upon as many men as possible. Magwitch pays for Pip to be trained as a gentleman and to exact his revenge upon Compeyson, the "gentleman" criminal.
6. Both characters employ Mr. Jaggers as their lawyer.
7. The most important similarity between the two is their influence upon Pip. Their relationships with him lead to his maturation and profoundly affect the novel's plot.