In Sir Gawain and the Green Knight, Gawain's positive virtues are similar to Beowulf's. He is loyal, first of all. He volunteers to take Arthur's place when the Green Knight comes to Arthur's castle and makes his challenge. He doesn't want Arthur to take the risk, and so accepts the Green Knight's challenge himself.
He is, therefore, brave. In addition to the events at Arthur's castle, his bravery is shown when he keeps his word, his promise, to seek out the Green Knight and allow the Green Knight to cut off his head, as Gawain cut off the Green Knight's.
Gawain is also trustworthy. When the castle owner's wife (the owner, of course, is really the Green Knight) tries to seduce Gawain, he politely refuses her offers.
These characteristics are similar to Beowulf's, but rather than outline Gawain's positive traits as they relate to Beowulf, I'll compare something more important.
Gawain and the Green Knight is an important work for numerous reasons, but one of them is that it portrays a hero that is actually flawed. Unlike Beowulf, Gawain is not perfect. First, he agrees to share anything he receives during his stay at the Green Knight's castle with the Green Knight. But, on the third day, after receiving a magic girdle or belt from the mistress of the castle, Gawain does not share that with the Green Knight. The girdle, according to the wife, has the power to keep Gawain from harm. Thus, Gawain doesn't give it up, not when he is on the way to have his head chopped off.
Second, Gawain flinches when the Green Knight's blade is descending toward his head. That may seem trivial to us today, but Beowulf-like epic heroes don't flinch. Gawain is more human, more realistic than Beowulf.
Thus, this narrative is an important step in the advancement of literature in the English language, a step toward literature as we know it today.