What are some differences between Athena and Penelope in The Odyssey?
Both Athena and Penelope are quite clever, but Athena is ultimately capable of commanding men and Penelope is not. Athena successfully manipulates the gods to allow Odysseus to finally come home (and escape the lusty Calypso); she instructs both Telemachus and Odysseus (instruction which they accept), and she is generally successful in all her pursuits, including keeping the peace in Ithaca at the end of the poem (when the suitors' families are enraged by their ignominious deaths and attempt to wage war on Odysseus and his family). Penelope is ultimately unable to keep the suitors from plundering Odysseus's stores, slaughtering his livestock, drinking his wine, and so forth. She deceives them for a while, insisting she will marry one of them when she completes the weaving of a burial shroud which she unravels a little each night so that she never finishes. However, the suitors find out and force her to complete it. Athena can get her own way, but Penelope really must rely on her husband and son.
The only power that Penelope has is her wisdom. She is a bright woman. She was clever with the weaving of the shroud for her father-in-law and with testing Odysseus at the end with her trick of moving his bed. However, she does not have any of the strength or warrior knowledge that Athena has. Athena is the goddess of war and wisdom, is known for her scheming and her craftsmanship.
As for relationships, Penelope has the love of Odysseus and always will. Athena shows love towards him (or perhaps it's just admiration), although she never pursues him in that way. Athena came directly from the head of Zeus--fully grown, etc. She is immortal. Penelope is a mortal, has a son, and will grow old and die with Odysseus.