My analysis of choosing Sir Gawain against Beowulf is that, Beowulf only happens to be strong on the outside. But Sir Gawain, along with his muscular build, contains a strong and stable heart. Beowulf goes to the land of the Danes and becomes a hero by his physical actions, with what he has done with his own hands. On the other hand, Sir Gawain has to make responsible choices to save his life and he makes the right choices not knowing that the King was indeed the Green Knight.
On the other hand, I still chose Sir Gawain rather that Sir Lancelot because Lancelot's reputation seems doomed from the start of the tale. Lancelot's behavior is far like a knight and not chivalrous compared to Gawain who, in this story is the perfect courteous and courageous knight. When Gawain brings Lady Ragnell to Carlisle he ignores the horrified reactions of the crowd and presented her to the king and queen as if she had been the fairest lady in the entire world.
In conclusion, through the Green Knight's tests, we see that Gawain is not the perfect knight he strives to be. Not even we, nor the Green Knight, nor his colleagues in the Knights of the Round Table informed him towards this standard of excellence. We read on the subject of the chaos Gawain encounters thinking about his imminent death at the hands of the Green Knight, and we recognize why he recognizes the girdle.