Your question is vague so I'm not sure exactly what you're after, but I'll see what I can do.
Both the Anglo-Saxon Beowulf and the medieval Sir Gawain and the Green Knight are written in alliterative verse, poetry that is unified by alliteration. Chaucer's The Canterbury Tales, contemporary to Sir Gawain, is written in iambic pentameter, in contrast. The Gawain poet writes in the style of the Anglo-Saxon Beowulf, hearkening back to the Anglo-Saxons.
One central difference between the two works, however, is that Gawain presents a hero with flaws. Beowulf, the character, is flawless. As such, he is mythical and totally unrealistic. Gawain, the character, is certainly still idealized and unrealistic, but his flaws represent a small step toward realistic characters. Gawain flinches when the Green Knight's blade is descending toward his neck, and fails to share the magic girdle with the castle owner as agreed ahead of time.
These are small faults by our standards today, but they represent failures in chivalry, and thus are a step toward realistic characters. Beowulf has no such faults.
The Gawain poem also represents a progression toward the achievement of realism. Contrast Beowulf's battle with Grendel, for instance, with Gawain's beheading of the Green Knight. The battle is related mostly by its effects: on the mead hall and the other men. Concrete detail is lacking. In contrast, concrete details dominate Gawain's beheading. Though the poem is idealistic and involves fantasy, the events are related with realism. This, too, is a progression beyond what the Beowulf poet achieves.