Thanks!
It's not necessarily
planning - I've used a lot of pre-written scenarios in Prince Valiant because the rulebook includes them, and when I got it (via Kickstarter) it shipped with an Episode Book that had more of them. But some of the ones in the Episode book need reworking (like the Rein*Hagen one, which is unplayable as written) and I've also come up with stuff spontaneously when I've needed it.
But Prince Valiant is not all that character-driven. Edwards, in
his essay on narrativism, distinguishes character, setting and situation as sources of (what he calls) premise; which, in Baker's formulation, is
the source of the conflict across a moral line. In Burning Wheel that's the PC, and because the core mode of PC build in BW is
by the player, the player plays a big role in establishing what the conflict and the moral line will be.
Whereas in Prince Valiant, the main source of premise/conflict is
the situation, which is generally presented by the GM, so (as I think you've intuited) the player plays less of a role in establishing that.
In my Prince Valiant game, as play goes on and the characters get more established, character as a source of premise/conflict increases. But in BW it's there from the start.
Burning Wheel can be played in a way where the GM establishes the conflict (at least at the start) and the players' role is then to play it out according to their authorship: namely, by having the GM prepare pre-gens and an initial situation. This is how the demo module The Sword works (that got discussed somewhere upthread). And here's an example of that that I wrote, in the same context ("Not the Iron DM") as After the Battle: