Beowulf the poem and Beowulf the movie (the 2007 adaptation by Robert Zemeckis) differ greatly when it comes to the characterizations of Beowulf, Grendel, and Hrothgar. In a sense, the movie changes the characters so much that one would not recognize the characters in the epic itself.
In the poem, Beowulf is Christian, humble, and an eloquent speaker. He gives his victories over to God, praises God openly, and speaks as a leader should. He leads a chaste life, focusing upon being the best warrior and king he can be. Given his faith, Beowulf lives a life spent in the light of God.
In the movie, Beowulf is far from humble. He screams of his victory by announcing "I am Beowulf!," not giving the glory of the victory to God. This also shows his lack of humility. In the movie, Beowulf has two affairs--one with Hrothgar's wife (Wealtheow) and one with a servant of Wealtheow (after they have married). This does not speak of living a chaste life. Lastly, Beowulf is characterized as living in shadow (he is given the nickname the Dark Wolf by Grendel's mother). Grendel's mother is even shown a possessing light, while Beowulf is shadowed in darkness (a distinct twist of the poem's use of light and dark).
In both the movie and the poem, Grendel is portrayed as the villain. This said, the poem explains his current state as being linked to his exile from God's light. The movie, on the other hand, fails to show this fact. The poem shows Grendel's attack on Heorot as the result of Grendel's hatred for God. The movie depicts his attack as the result of an infected ear drum (which the people's singing hurts). While somewhat similar (given the singing acts as a trigger in both the poem and the movie), the Christian perspective is removed from the movie.
In the poem, Hrothgar is a Christian. His praise of God is so great that he even builds Heorot to praise his lord. Hrothgar proves to be a very good king who follows the true Anglo-Saxon code.
In the movie, Hrothgar fails to come close to the character portrayed in the poem. In the movie, Hrothgar openly denounces God (stating that he and his kingdom will stay Pagan). Hrothgar is also portrayed as a drunk in the movie. He fails to be a good husband (leading his wife into the hands of Beowulf) and commits suicide.
The link below shows the movie version of Beowulf "introducing" himself to Grendel. Notice how he states that he is the "chief of the darkness" (contrasting the image of light he should possess according to the poem).