The three heroes discussed here, Beowulf, Sir Gawain and King Arthur, are heroes for different reasons. Beowulf, our earliest hero, is brave but his motivation is different than then other two. To Sir Gawain personal honor and valor is what is important. King Arthur, Sir Gawain's uncle, is naturally the quintessential king of the medieval period. Though all men to a certain extent share the same qualities, some are more pronounced than in the others. It is important to see how these qualities are central to their respective stories and how it helps (or hinders) them in their journeys.
The greatest value of Beowulf is his bravery, some may say bravado. There is no doubt that he is a great warrior. Beowulf's heroism belongs to a different time than that of King Arthur or Sir Gawain. For that reason his bragging about his prowess might seem decidedly unheroic.
When he tells Unferth "I count it true that I had more courage, More strength in swimming than any other man" (514-15 (41) it might be interpreted in a poor way. What he is saying though is true. In addition, in order for him to succeed he must orally deliver his resume. Nevertheless, bragging aside, Beowulf is undoubtedly a brave man. When Beowulf sets out to kill Grendel's mother he simply "donned his armor for battle, Heeded not the danger..." (1328-29 60). When his sword fails him he uses his physical strength: "On the might of his hand, as a man must do Who thinks to win in the welter of battle Enduring glory; he fears not death" (1420-23 62). Certainly he is in search of fame. Though this is true it must not discount his brave actions. He gains his fame truthfully by doing battle with menaces to society.