What is interesting about the comparison between these two characters is the way that Odysseus is shown by Homer to be a character who definitely has to learn a number of important life lessons during his journeys concerning his arrogance and pride, and his men are shown to suffer directly as a result of his rash braggadio and rather foolish decisions. This is something that is most apparent in the way that Odysseus taunts Polythemus, having blinded him, therefore giving the cyclops the ability to ask his father, Poseidon, god of the sea, to curse him and make his return journey very difficult:
Cyclops, if any mortal man ever asks you who it was that inflicted upon your eye this shameful blinding, tell him that you were blinded by Odysseus, sacker of cities. Laertes is his father, and he makes his home on Ithaka.
The arrogance and stupidity in giving a defeated foe such information is something that Odysseus later comes to regret after the intense suffering that he and his men experience, especially considering that he looses all of men as a result of this arrogance.
This aspect of the character of Odysseus is something that makes him very different from Beowulf, who is much more a stereotypical epic hero in the way that his strength, valour and skill is described. There is very little sense of Beowulf developing as a character and learning from his mistakes, as Odysseus does, and he enters the epic with the same level of skill and bravery that he demonstrates throughout. Note for example how he consistently makes tasks more challenging than they need to be, by refusing to use weapons in his struggle against Grendel for example:
I have heard moreover that the monster scorns
in his reckless way to use weapons;
therefore, to heighten Hygelac's fame
and gladden his heart, I hereby renounce
sword and the shelter of the broad shield,
the heavy war-board: hand-to-hand
is how it will be, a life-and-death
fight with the fiend.
Beowulf by doing this wins more honour for the Geatish king through his eschewal of arms, but also transforms what is a battle between good and evil into a battle of skill. It is a matter of personal pride for him that he does not have any special advantage over Grendel as he comes to fight him, and thus he demonstrates typical traits of the epic hero. However, there is very little sense of him developing as a character in the course of this epic classic, as there is with Odysseus.