In "Rappaccini's Daughter," the two primary characters are Beatrice and Giovanni. They end up in the same place, but they're certainly more different than alike.
Beatrice is the daughter of a doctor and lives in Padua. She is beautiful and trusting and rather naive because she has not been exposed to any of the world beyond the confines of their garden. People in the town are under the impression that she has been studying medicine with her father; in fact, though, she has little knowledge of anything beyond caring for the flowers in the garden. She enjoys spending time with Giovanni both for himself and for the knowledge of the world she learns from him, like a child soaking it all in. She understands her circumstances, to some degree, and is saddened but not surprised when she wilts flowers and kills insects by her touch and breath. She appears to genuinely love Giovanni.
Giovanni has come to Padua to study at the University. He is not wealthy, as he only has a few gold ducats in his pocket and a letter of introduction when he arrives. He is homesick upon his arrival and is cheered at the sight of Beatrice in the garden. He is warned that Dr. Rappaccini is a scientist who cares more for his experiments than the patients whom he treats. He dismisses this information and continues to pursue the lovely Beatrice, even when he sees evidence that she can wilt flowers and kill insects. He enjoys spending time with Beatrice, teaching and talking with her about many things, but never touching. He does appear to love Beatrice--until he thinks he's been duped by by the Rappaccinis and has been poisoned.
At this point, though their stories aren't particularly similar, their paths converge. Beatrice is infuriated at what Rappaccini has done--"created" an artificial world in which these two people will be powerful and untouchable...and forever isolated from the rest of the world. Once Giovanni realizes that Beatrice is an innocent pawn he forgives her; and he, too, is infuriated with the doctor. It seems to me this is really the only point of comparison between the two of them.