To read Part 1 of this little comparison, click here.
Now that I have compared Caspian to King Arthur, let's move on to the events that take place after the two are established as rulers. Arthur has his knights set out on a quest for the Holy Grail that takes many years and involves many shortcomings from said knights. Caspian's people have been searching for Prince Rilian, who was stolen by the Lady of the Green Kirtle as a child. This search, too, takes many years.
It is only someone pure who is able to take the Grail--and isn't it similar with who is able to find Rilian, as well? Jill and Eustace are, at least, both children. Questers for the Grail also see visions, which they must interpret. Jill and Eustace are constantly having dreams or other messages from Aslan--which they usually misinterpret or forget or otherwise mess up. They have a very Grail-Quest-like guide, too, in Puddleglum.
I think also there is similarity in the tone. The Silver Chair has never been my favorite Narnia book, but I may find it the most relatable. The characters just never seem to do things right. But there is also a peculiar tone to this book that is simultaneously disconcerting and compelling. It is enhanced by both many harsh weather scenes and much magic--both the evil magic of the Lady of the Green Kirtle and the good magic of Aslan. These are "extraordinary events" that constantly come into the King Arthur legends, as well. The Lady of the Green Kirtle is not so different from Morgan le Fey, Arthur's half-sister and mother of Mordred (who gives Arthur his deadly wound). Both are women gone wrong whose enchantments must be overcome.
Once both quests are played out, the kingdom is brought to a better place--at at least out of the slump it was in before.