It's a lot easier to contrast the characters of Beowulf and Grendel than it is to compare them, so let's do the hard part first and look at how they are similar (comparison).
Beowulf and Grendel both embody the characteristics of their archetype (an archetype is a kind of literary element that becomes a pattern over the course of many years). Beowulf is the epic hero, and as such possesses the characteristics of bravery and exceptional strength. He stands out among men as a singularly impressive warrior. He is also committed to the ideals of his archetype. Grendel also fully embodies the characteristics of his archetype—which we will call the “villain,” for lack of a better term. Like Beowulf, he is fearless, at least initially, and when he sets out to do battle he fully expects to succeed.
Contrasting Beowulf and Grendel is easier. Obviously, one is human (Beowulf) while the other is supernatural (Grendel). Beyond this obvious difference are their contrasting motivations. Beowulf wants to achieve everlasting fame and to live in accordance with the warrior code (sometimes called the Heroic Code) of his era. As a warrior, he is part of a social structure that values the character qualities and warrior skills that he possesses. Grendel, on the other hand, is not part of an established social structure. He is born of a cursed race sired by Cain. He is an outcast. In fact, early in the poem, Grendel's motivation for attacking Herot is shown to be his anger at the noise they make during their celebrations—he does not like the fact that they gather together in fellowship. This makes him a threat to the society that Beowulf values and strives to protect.