This is a very interesting question to consider, as the heroic tradition in literature has definitely moved from epic heroes, the creation of larger-than-life characters who had legendary strength and physical characteristics, to the move towards anti-heroes, which particularly developed in the 20th and 21st centuries, with the focus on leading protagonists who lack certain heroic qualities, such as idealism, courage and generosity. 

When considering Beowulf as a character, it is clear that his exploits and fame confirm his as a character whose strength is certainly out of this world, and more powerful than any other character alive today. This shows he is definitely a hero in the epic hero tradition, as he arrives at Herot with this strength and we see little development or change in him in terms of his physical prowess. Note, for example, how he gives an account of his struggle with Grendel and how he tore Grendel's arm off during this fight:

The Lord allowed it, my lock on him

wasn't strong enough, he struggled fiercely

and broke and ran. Yet he bought his freedom

at a high price, for he left his hand

and arm and shoulder to show he had been here...

Beowulf's strength is so great therefore that Grendel had to literally part with his limb in order to escape him. This feat for an ordinary human would clearly have been impossible, showing Beowulf to be a perfect example of an epic hero who possesses qualities that cannot be replicated by mere mortals. 

However, if we compare Beowulf with a heroic figure such as Thorin son of Thrain, who is a hero in many ways in terms of his strength and valour in battle against numerous foes, it is clear that there is a sense in which he can also be considered to be an anti-hero, as Thorin has one major fault that comes to dominate the plot of this novel. It is Thorin's greed and how this consumes him that threatens the whole expedition and the dwarves. His obsession for finding the Arkenstone and for keeping the former wealth of his people shows that he is more of an anti-hero than a hero, as he is not able to see his greed and how this impacts the other characters around him. Note for example what he says about the Arkenstone:

For the Arkenstone of my father... is worth more than a river of gold itself, and to me it is beyond price. That stone of all the treasure I name unto myself, and I will be avenged on anyone who finds it and withholds it.

It is Thorin's greed that leads to the dwarves and Bilbo being besieged by themselves against a whole army of men and elves, and it is this situation that leads Bilbo to deliver the Arkenstone to the humans and elves in order to secure peace. In Thorin, therefore the development of the anti-hero can be seen, as he is a character who has many heroic properties, but has one major failing that comes to dominate him: his greed.