Beowulf's story is being told by Christian tribes. He finds nature on his side because God is on his side - and he works within Gods will. He does not fight gods or nature, but rather only fights irrevocably evil demons. He is associated with a pious culture which is not humanistic, and in which science and other such forms of hubris are not encouraged. Beowulf is a truly medieval hero, just as Odysseus was Grecian.
This difference in culture, between the material and the heavenly, is seen in every aspect of the two characters and their lives. It exists also in their ends. Odysseus spends his entire story seeking a way home to the home of his body - to his wife, his child, his fields and bed. Beowulf is seeking only the ultimate good, and he turns down physical reward and even resists kingship until...
Throughout the work, he seems almost eager to die. Odysseus is always on his way home while Beowulf is always on his way to his death, because Odysseus is a man of this world and Beowulf of the next. Thus not only their characters, but also their plot arcs, may be seen as indicative of the greatest values of their cultures, whether that be focused in the physical, lusty now or in the abstractly good Hereafter.
Bibliography used different translations of these two books, so as to make them searchable and because I could not access the specific textbook
Beowulf. Trans. Dr. David Breedan. Archived at http://www.lnstar.com/literature/beowulf/index.html
The Odyssey by Homer. Trans. Samuel Butler. Archived at http://darkwing.uoregon.edu/~joelja/odyssey.html
