Compare and contrast the characterizations of the Wanderer and Beowulf (the characters, not the poems).
Beowulf and the Wanderer are similar in a few ways. They are essentially the same character at very different points in life. Both characters are warrior types that fight for a lord of some kind. They both revel in glory, honor, and good companionship at a mead hall. Finally, both men know what it feels like to lose fellow warriors and a worthy king. That king in Beowulf is Hygelac, who also happens to be related to Beowulf. The lost king in The Wanderer is not named, but the text does show that the Wanderer laments the loss.
Among the living
none now remains to whom I dare
my inmost thought clearly reveal.
The difference between these two characters is that Beowulf is currently surrounded by fellow warriors, glory, honor, and companionship. He is at the top of his game, and he is capable of protecting himself and many other men. Praises are heaped upon him for being courageous and strong. None of that applies to the Wanderer. He may have had all of that at one point, but he has lost all of it. Consequently, he is filled with sorrow and quite lonely. He longs to return to his former glory as one of a lord's brave warriors.
where far or near
I might find one who in mead-hall
might accept my affection, or on me, friendless,
might wish consolation, offer me joy.
It's possible that Beowulf could have some day ended up like the Wanderer, but as we see Beowulf throughout the poem, he is confident and hopeful of the future. He believes that he is capable of meeting any kind of challenge head on. On the other hand, the Wanderer seems to be beaten down by his situation. In fact, as the poem closes, the Wanderer even contemplates how death would be nice because it would end his sorrow.
Well will it be
to him who seeks favor, refuge and comfort,
from the Father in heaven, where all fastness stands.
That's not something that Beowulf would have said. The only thing Beowulf wants out of death is a glorious death in battle.
The characters you ask about are both products of Anglo-Saxon poetry, of course, and are actually related in a specific way. The Wanderer is an example of a character orphaned, in a sense, when his mead hall is destroyed, or his lord is killed, or he is, in effect, exiled for some reason. The Wanderer is like the characters that would have fled from Grendel. Grendel is representative of that which can destroy a mead hall and orphan its inhabitants, like the Wanderer.
Beowulf, in contrast, is a hero that keeps mead halls from ruin. He is a super hero, so to speak. He is big and pure and courageous and unbeatable in battle. He conquers Grendel, not victimized by him.
The Wanderer is motivated by companionship and security. Beowulf is motivated by his desire to be remembered. The Wanderer is a homeless laborer, while Beowulf is king material. The Wanderer is realistic, while Beowulf is an ideal.
A cultural connection, then, exists between these two characters, but similarities are few.