Beowulf is a very confident character as he demonstrates when makes bold claims like fighting a giant mutant monster with his bare hands. Beowulf's "cocky" personality can come off in modern times as arrogant which is a negative character trait. Back when Beowulf was written however, the trait of full confidence in one's self could have been viewed as an admirable trait. When we look at heroes in modern stories like Harry Potter and the Chamber of Secrets by J.K. Rowling, the main character, Harry, is not very confident at all. Harry must overcome many dangerous tasks that he is very scared to do, things that Beowulf would do without a second thought. For example, when Harry must play in the Quidditch match, he was intimidated by the opposing team, Slytherin. Rather than cower in fear upon seeing Slytherin, Beowulf would have challenged their best player to a one-on-one brawl. Between now and the time Beowulf was written, the way a hero is constructed in literature has "flip-flopped" in terms of character traits.
Another difference between modern heroes and ancient ones is that modern heroes have some sort of back story. In Harry Potter's case, his parents were murdered by Voldemort and he was saved by a special spell his mother set on him. He lived with his Aunt Petunia, Uncle Vernon, and cousin Dudley. Harry was neglected and unaware of his wizard powers until an old friend came to take him off to wizarding school. The back story to a hero has become a must for modern stories because it gives the audience a better understanding of that characters' actions and behaviors. Since Beowulf didn't really have any sort of introduction or back story, the audience doesn't receive a good connection with the character. The lack of these of elements reveals that society didn't much care for a history lesson about the main character and they just wanted to get to know the character through his/her actions.
A similarity between modern and contemporary heroes is that they both follow the classic hero story outline. They both have the call to an adventure. For Beowulf, it's Hrothgar calling him to help be rid of the evil and monstrous Grendel, and for Harry, it's Hagrid who literally calls out to him to join the wizarding world. Both characters are tested on their journey that make them learn some sort of lesson. In Harry's scenario, he must defeat the evil and convoluted Voldemort and for Beowulf, he must defeat Grendel and his ferocious mother.
The differences in the ways heroes are constructed in modern literature and ancient literature are plentiful and show how society has changed its values. The character traits of new heroes to old ones are completely flipped revealing that modern society likes to root for the underdog and not the defending champion. Literature has remained steadfast however, in the structure of the hero's journey. All heroes are called by some sort of outside force and are tested throughout their journey which always has some sort of insightful meaning behind it.