Yeah, I didn't figure you meant "narration authority", but as I started trying to address what you *were* talking about, I realized that no examples came directly to mind, so I tried to get my brain going by coming at it sideways-like.
At any rate, I haven't yet played Mouse Guard either, just given a read through, but if my understanding of the rules and some of the actual play reports I've read is correct, then basically a session has a "GM's Turn" and a "Players' Turn". The GM's turn is the actual mission, and the dialogue is structured pretty traditionally with the GM setting scenes, describing dangers and challenges, and asking the players what they do and otherwise prompting them as necessary.
The Players' Turn, on the other hand, is the sort of end of session/between mission downtime. The players are explicitly instructed to describe their own undertakings to heal, train, and other "taking care of business" actions. The number of actions you get is affected by checks you earned during the mission and goes round robin between the players. In this phase, the players frame scenes (with some help from the GM if they want it) describe what they're up to, and call on the GM to oppose any tests they make for things like training. Again, this is just from my remembering what I've read through once, my rulebook is at home in another state.
I also haven't played Archipelago yet, but it's pretty exciting to me. Thinking about it some more, I believe that even more significant to the "flow of conversation" thing you're talking about than the round robin scene framing might be the ritual phrases. If you're not familiar, they're things like "That might not be so easy. . .", "Try another way", and a few others. What it seems like they do (anybody more familiar with the game, please correct any deficiencies I put forth) is to give specific permission to do things that people collaborating creatively will do - interrupt to offer better versions, ask for more detail on something that seems cool or unclear, and so forth. I feel like that will have a more subtle but important impact on the way the player to player interactions go than the more "story significant" rules that have each player take turns framing a scene and controlling the extras.