Yes, the challenge decks have a much stronger narrative theme to them than a normal game. The Dark Side challenge deck has the Light Side players trying to prevent the activation of the Death Star II, and if things go badly, destroying it before it can eliminate the Rebellion. The Light Side challenge deck (roughly) follows the events of Shadows of the Empire, and has the Dark Side players searching for Luke Skywalker after his escape from Cloud City.
Both challenge decks require (or at least strongly suggest) the opponents tune their decks to deal with it.
That said, I have no idea how those translate into the solo rules.
They play pretty well solo and even better with JK's ideas, the hottest download (500+) for this game.
As these have a fixed objective there is not much call for subtlety.
Although each game as a whole really represents a campaign over a period of time , involving espionage, feints , battles and god like intervention (The force). Thematically it is best not to think of it as a single battle. One of the most underrated LCG's. So much easier to deck build than the others.