There is actually not a "correct" response to this question, because it asks for the writer's opinion. It is actually a combination question, because the writer must argue persuasively, as well as compare and contrast the two characters.
The important thing to do when you write your response is to support your answer with specific evidence from the story. For example, if you are of the opinion that Penelope suffered more than Odysseus, then you need to explain why she did and give some examples of how she suffered. A top-quality response would also include an explanation of how Odysseus's suffering did not exceed Penelope's, which would require that you also give some examples of his suffering.