If the story and the threads interest me I don't really mind if I can't add to the story myself. However nonetheless I have found myself gravitating towards public, moderated, private stories in that order.
Thinking why that is, personally for this site, I like the CHOYA aspect of stories rather than a single plotted story thread (even if it is actually a good story).
Based on experience as a reader I do mentally flag that there are probably going to be less choices to make in a private story vs public or moderated.
That said these days I generally do a quick scan of the story map anyway.
The other thing I've noticed is that individual Chapter lengths end up being a lot longer in private story. I'm more inclined to read Chapters in chunks rather than a wall of text.
So mode doesn't matter as such but they do tend to corrolate towards different presentation meaning I often prefer public.
However as a reader I'm approaching this site from the point of view of wanting erotica/porn (with a bit of a story) and lots of variety.
Plenty of members are looking for well structured, written and coherent stories. Private probably lends itself better to that (There's a reason there are few novels that have more than one author).