Published scenarios for Prince Valiant - Episodes is the technical term - are generally a single situation: the PCs encounter a knight who won't let them cross a bridge without jousting, or meet a strange traveller who turns out to be the ghost of a merchant killed and robbed by bandits, or similar.Well, I cannot speak to the referenced AP, I know nothing about it. However, this sort of thing is VERY tough for adventure writers to pull off, at best!
my point is, adventures are pretty strongly constrained to have a rather narrow fixed set of contemplated outcomes. Going 'off the rails' or heavily customizing is cool. I think they can provide some material, but honestly its hard to see very many successful adventures in any classical sense being written for most Story Now play. Something like @pemerton's favorite Arthurian Romance game, Prince Valiant, is probably about as ideal as it gets, the sorts of action that happens in that milieu is pretty strongly stereotyped, and a lot of what matters is more HOW you did something and what its effects on the character were, vs lots of doubts about the basic plot and who will fight who, when, and where.
In the Episode Book, which was part of the reprint Kickstarter a few years ago and has an all-star cast of contributors, there are some episodes that are more railroady. (I've posted about this before, so won't repeat myself unless you or anyone else is interested.)
I think the key thing about most of the scenarios is that they permit multiple pathways out. In our game the PCs did avenge the murdered merchant. They defeated the demon possessing the Crimson Bull by calling on the holy power of St Sigobert, thus sparing the bull from sacrifice and also converting the Wise Woman in the process. They helped the Crowmaster's apprentice elope with his beloved and set him up with the lord of Castle Hill as a new Crowmaster. At Fort Seahawk they were unable to prove the perfidy of the lord's brother, and so subsequently heard that the lord had met an untimely death, obliging his brother to take over as the local ruler. And in our version of the (de-railroaded) Mark Rein-Hagen scenario, the PCs ended up taking control of the disputed castle and Duchy by way of the marriage of one of their number to the daughter of the deceased Duke.
Any other Prince Valiant game seems likely to involve the same sorts of events - jousts, sieges, marriages both romantic and political, etc - and naturally, if using these Episodes, the same NPCs and antagonists. But I'd expect the actual resolutions, and the overall shape of the campaign, to be pretty different. To draw an (imperfect) comparison to D&D, I'd say it's more like open-ended play in B2's Keep, than working systematically through the Caves of Chaos.