The epic Beowulf illustrates the constant battle between good and evil. Within this battle, conflict is forever present. This said, the conflict which exists is not only external (man verses man, nature, or supernatural), the conflict which exists can sometimes be internal (man verses himself).
External conflict is much easier to recognize. Any conflict which arises between two different people, beings, or elements is considered external.
Beowulf- Beowulf faces many different external conflicts within the text. Not only does he face Grendel, he faces Grendel's mother, a dragon, sea monsters, and the ocean (during his swimming battle with Brecca). As a true hero, Beowulf succeeds in defeating all of the challenges and foes he faces (although his battle with the dragon does end Beowulf's life).
Grendel- Grendel faces three main foes within the text. While the conflict with Beowulf is obvious, he also conflicts with the people of Heorot and God.
Beowulf- Beowulf essentially fails to show any true internal conflict. In fact, he is so confident in his ability and God's power that, he accepts every challenge without thought. Even in his death, Beowulf does not question (or conflict with) what is happening to him: "he knew full well that his portion of earthly bliss was done and gone" (Chapter 37).
Grendel- As for Grendel, he faced much internal conflict. Given that he was exiled from God's light because of his ancestor Cain, Grendel hated God and those who celebrated him. Therefore, his hatred of God led to his possession of a terrible internal conflict--he hated God so much that he took this anger out on the people of Heorot. Not only that, when fighting Beowulf, Grendel is surprised by the utter strength of the warrior. When faced with the decision to fight or flee, Grendel flees the battle (leaving his shoulder behind as a trophy).
Both characters struggles with internal and external conflict although they recognize it differently. Beowulf has less internal conflict with his actions. He sees his murderous ways as necessary to keep order in the kingdom and to advance his "career". Grendel is his largest external conflict. He believes he is doing the noble thing by killing Grendel and keeping the men safe. Grendel does show moments of internal conflict when killing the men. He doesn't want to kill them, but they are his source of food, so he feels it is necessary. He has multiple sources of external conflict simply for the fact that he is seen as a monster. He views any violence against those as simply self defense. The most notable humanization comes when he grieves his mother, for which Beowulf shows no conflict.