In terms of personality, these two are quite radically different characters—Pip is personable, friendly and well-liked, while Heathcliff is brooding, enigmatic and bad-tempered. So I think comparisons will mainly be drawn between the characters' life circumstances.
Both are orphans—but Pip is taken in by his own sister and her husband, while Heathcliff is a foundling, raised by the Earnshaw family, who are of a far higher social class than he is by birth.
Both characters are born into relative poverty.
Both rise to a higher social class due to the assistance of wealthy beneficiaries.
Both are treated as if they are little more than servants because of their class, originally—Pip by Estella, who thinks she is below him, and Heathcliff by Edgar.
Both fall in love with women of higher social classes.
Both are thwarted in their love—however, they deal with this in very different ways. Pip accepts that he and Estella will never be together, and they part on good terms; Heathcliff pursues a vendetta which ultimately consumes him with jealousy.