From the outside, the two could not be more different. Odysseus is a mighty man, known for his prowess and bravery in combat and in various tough situations. Winston is a small, graying man with physical ailments and living a life full of fear. Odysseus takes pleasure in confronting the gods and trying to win in impossible situations. Winston is thrilled that he is willing to write in a journal that no one knows about.
But they are both struggling against overwhelming odds and both act with great courage. Whether it is Odysseus struggling to find a way to defeat the Cyclops or Winston trying to resist the work of O'Brien as he is being tortured, they both have struggles that fit the classical idea of a hero.
The other similarity, according to some critics of Odysseus, is that both Winston and Odysseus are completely focused on themselves. In some ways Winston does this in response to the overwhelming pressure to forget yourself and love Big Brother and Odysseus does this simply because he is selfish and always looking to satisfy his own desires. But they end up with the same desire, to save themselves from the difficult situations they get themselves into.
At the close of each story, their paths diverge as Odysseys has a triumphant homecoming and Winston waits for the bullet that will end his life. In this regard Winston better fits the classical model of hero in which he must die so that a hero cult can grow around his memory. But Odysseus being one of the prime examples of a hero in classical literature also lays claim to heroic status by the way that he returns home, vanquishes the suitors and retakes his place as the king in his own hall.