What character could Sir Gawain be compared/contrasted to in Morte Darthur and what are those contrasts and comparisons?
You could pick numerous characters to make the comparisons you're asking about. I'll pick one.
Sir Gawain in Sir Gawain and the Green Knight is noble and chivalrous and possesses all the traits a knight in a medieval tale is supposed to possess. So does Sir Bedivere in Morte d'Arthur. The interesting characteristic they have in common, however, is that they both faulter.
Sir Gawain makes mistakes: he fails to share the magic girdle with the castle owner as he promises he will, and he flinches when the Green Knight's blade comes down toward his neck. Sir Bedivere fails, in a sense, also. When Arthur orders him to throw Excalibur into the lake, he chooses not to--twice.
Both characters redeem themselves, however, and are found noble in the end.
Gawain, of course, though, fails his tests in an attempt to save his life. Bedivere fails his test of loyalty and obedience because, he says, throwing the sword in the lake will bring only bad, while keeping it will bring good. Of course he says this right after he notices the jewels in the sword.
Those are some comparisons and contrasts between the two characters. I'll let you decide whose failure is more noble.