Beowulf’s mission was fairly different.
As the monster Grendel was terrorizing Herot, Beowulf sets out to help Hrothgar. It can be suggested that Beowulf is seeking fame and glory that will, in a sense, give him eternal life. Beowulf, before fighting Grendel's mother, proclaims, "Each of us will come to the end of this life on earth; he who can earn it should fight for the glory of his name; fame after death is the noblest of goals." After cutting off Grendel's claw and head he pursues the monster to make sure that he is dead, and when Grendel's mother seeks revenge he doesn’t hesitate to fight her. He originally sets out to help Hrothgar and does not intend to leave the quest unfinished. Again, near death, he thanks God for all the treasure and requests to have his tomb at the water's edge, so sailors can see it and remember it as 'Beowulf's
tower.' Beowulf is very irrational and inconsiderate as well as greedy and superficial. The true reason why he sets out to help Hrothgar get rid of Grendel and his mother is his personal quest for glory and fame. Both Gilgamesh and Beowulf may be brave and determined enough to go on quests in search for a great treasure, but only one, Gilgamesh, is doing his quest for the right reasons. He’s already a king and known, why should he want to be known even more by defeating a monster. Beowulf being an irrational and selfish man doesn’t seem to be idealistic qualities that the citizens would want there leader to be. He’s a great person but not an epic hero. Gilgamesh is the ideal true epic hero.