It seems that Penelope has more power over Odysseus in The Odyssey than the goddess Athena because she loves him and he loves her. While Athena is a goddess and experiences a closer than normal relationship with Odysseus, much closer than the typical god/goddess and human relationship due to his hero status, there is nothing in this relationship to compare to the sacred relationship Odysseus shares with his beloved wife, Penelope. She has loved him and waited for him for twenty years, and this combined with her unrelenting belief that Odysseus will return, gives Penelope a surprising amount of power over her husband.
Love is a powerful emotion, and love is the force that drives Odysseus to return to Ithaca and, more important, Penelope. No matter what obstacles are put in his way, he remains steadfast in his desire to go home to her. Those obstacles are created by Poseidon, whom Odysseus has offended, and they are removed by Athena, who is Odyssues's patron goddess. I'm not sure it is correct to say that Athena and Penelope compete for power over him; they are both interested in seeing him regain his throne. Also, Athena is the patron of the "womanly arts," which is what Penelope is doing when she weaves. Athena also encourages their son to cause as much trouble as possible with the men who are vying to marry Penelope, keeping her free until Odysseus returns. So you might say that Athena and Penelope share influence over Odysseus.
Penelope didn't have more power over Odysseus. They experienced true love for each other but met in a like-minded way. Athena shared a different relationship where she guided Odysseus to Penelope. In fact Odysseus often outsmarted both women to get his own way. Certainly Odysseus was very loyal in his love for Penelope but listened to advice given by Athena. The power in fact lies lies with Athena for she was the Goddess and directed the fate of the mortals. The weakness of Athena was that Odysseus did not love her and Penelope had more power that way.