This is actually one of my favorite contrasts between The Hobbit & LotR and also pretty interesting because it deals with two of my favorite characters in all of Tolkien’s works! I always refer to them as the “crownless kings”, because while Thorin has bore more of a crown than Aragorn has, all the same it was taken from when he was relatively young and in turn, both are kings who have neither throne, crown, nor kingdom. However, I’ve always found their core sense of identity extremely interesting and I’d argue why Aragorn is the one of the pair who is able to reclaim his crown and rule peaceably and dutifully.
Now, this isn’t meant to be a sort of slight against Thorin. I love Thorin; he’s always been one of my favorite characters, but the contrast between his sense of self and Aragorn’s is striking. Throughout the Hobbit, time and time again Thorin is absolutely determined to announce himself as king, as King Under the Mountain. When first encountering the guards at Laketown after escaping Mirkwood, he boldly and proudly reveals himself, “Thorin son of Thrain son of Thror King under the Mountain…”. Time and time again, Thorin takes pride in his heritage and his identity as a king, a king who deserves a crown and a kingdom and his rightful gold and will have it. All his other identities, as a harpist, as a warrior, etc, all of these are far less important than his identity as a king.