I've read both and a few articles and still haven't formed a decent answer

Question

In what way is the character of Sir Gawain different from other epic heroes such as Beowulf?

Beowulf is Anglo-Saxon
Sir Gawain is Medieval

Beowulf is strong, monster fighting, courageous, a prince

Sir Gawain is chivalrous, knight, of least strength

Answer 1

Think of it this way: Does might make right, or does right make might? In most old legends, physical power overwhelms the enemy. In the Arthurian legends, being "right" and virtuous is mightier than the sword, even when physical power becomes necessary to defend what is right. How do Gawain and Beowulf fit into that dichotomy?

Answer 2

I see it as Beowulf is focused on "externalizing" power: strength, fighting, birth power.
Gawain has his focus on"internal" power: will, being"right" vs being strongest, the power of virtue vs physical power.

Remember Vietnam? The US came in on the side of a corrupt dictatorship, trying to win a war with overwhelming physical strength? While the North saw the war as a civil war, against a corrupt South goverment...a war of virtue which they won. Both sides had "heros", of very different strengths.