I sometimes like getting to see different characters reacting to the same situation - which you don't always get to see when everyone has a unique story.
But for the same situation/different characters thing to be engagement, the reactions and vibe of each character really have to differ substantially. I think that's the weakness of the overlapping route structure. It has the potential to be quite engaging, in my opinion, but it's really hard to execute that. (Speaking from experience, my "overlapping route" game has been SO hard to write. It's way, way harder than I thought it would be!)
I could ramble on about game structure for a long time, but that's more suited to Discord. LoL! I have a lot of thoughts about what makes the different structures fun to play and also what makes them fun to create, though.
I do prefer giving everyone their own story, though. So this one project will be the only one with overlapping routes. I'm glad I'm trying it out but I don't think it's my writing preference. ( •̀ ω •́ )✧