Bedrockgames
I post in the voice of Christopher Walken
Yeah, and I thought you made some pretty reasonable points. There IS, at least potentially, a continuum. I can just say that I haven't in 40+ years of play, actually experienced a D&D game that got to where the BitD game was the other day. I'm OK with the assertion that maybe once you get to a certain point there's some substantive reason to not formulate your D&D game exactly like, say, Dungeon World, that maybe you like some elements of GM direction and "OK, we'll play an adventure that reflects on PC concerns, but the GM will still draw maps and keys within that context" or whatever is where you want to be. I think there is just a tendency for some people to try to assert that there's no 'air' between that and something like DW or BitD, and I don't think that's the case. I think a more principled stand to take, which seems to be yours, is "Yeah, system matters, these are likely to play differently, and we can say different things about them." The semantic arguments beyond that point are fairly uninteresting to me, or at least I don't perceive any value in wandering in that particular swamp.
I think I would say "System can and often does matter, but it isn't the only thing, and there are ways to solve problems beyond just mechanics or system". I think what sometimes happens though is people see that and they read something more like "System is meaningless" which is far from my position.
I think the danger is to look at something like Hillfolk (and I am just leaning on that because I am familiar with it, whereas I can't speak as well on BitD), seeing that it allows players to do things like frame a scene and to establish facts through their dialogue, which granted is giving the player tremendous control (albeit they are constrained by some of the drama conceits of the systems as that is the focus, but they have a lot of control), and then take from the a dichotomy where anything in D&D is a railroad on one end because it doesn't afford that same level of imperium to the players in terms of narrative authority (and it doesn't place as many limits on the GM, but a game like Hillfolk offers total freedom. Because 1) there are plenty of other ways players can be empowered to help shape the course of a campaign in a traditional game, and 2) while Hillfolk offers players a good deal of power over these things, blurring that line between the character and the setting does have its costs (i.e. a mystery is an entirely different thing in this kind of campaign: it is harder to have an adventure where the players solve a mystery as a problem to be solved).
I should say I don't think either one is better or worse at mysteries. It really depends on what you want. Some people want to help create mystery and discover a mystery together, some people want to solve it. If you want to do the former, Hillfolk would be a better system than Cthulhu (at least in the editions I have played), but if you want to solve a mystery, I'd recommend Cthulhu.
But just because there is a mystery in a Cthulhu campaign, that doesn't mean there has to be one. You can use the three clue rule, you can say I am going to run a bunch of mysteries, but if you tell the players at the start of the session something like:
"I am interested in finding out what happens as much as you are. I don't want to feel like I am just handing you my notes, so I encourage you to smash the scenery, smash plots, explore your characters personal goals and motives, and I will honor that. I may not do exactly what you want or expect but I will lean in that direction. I am much more interested in something that feels like Fargo than something that feels like Sherlock Holmes."
You are going to have a very different experience and one where the player goals are more likely to have a large impact on the course of the adventure. Especially if the GM is also rolling everything in the open, not fudging, letting players kill whatever NPC or monster they legitimately can, etc.
You can also combine these two things. This is something I tried with Hillfolk because it has two types of scenes: Dramatic and Procedural. So we used the Dramasystem from Hillfolk for Dramatic Scenes in a campaign but used my own system (which is more on the trad end) for Procedural scenes (dramatic scenes are more about the internal drama and characters resolving conflicting goals, whereas procedural scenes are more about external things like stealing the Raksha manual from the Zombie Sect headquarters).