Private groups allow you to have discussions you can't have on the mains, and they are often moderated in a way that members find more agreeable (i.e. certain things that aren't allowed here are allowed there, but things that are allowed here aren't allowed there). It's easier to keep out trolls who make dozens of alts every time they're banned, and it's easier to forge connections with members because of the smaller community size.
I mean, I like the mains well enough. I like venturing out and seeing opinions and perspectives that private groups generally weed out over time. But were I forced to choose one, I'd choose private groups any day. Curious to see which choice others would make.
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I've never really found any difference in quality/intelligence/etc between any private groups and the mains. Only difference is activity and some limitations on subject matter. I'll frequent the more active forums more and the less active ones less. The restrictions on subject matter don't bother me because they're better left out of the reach of, well, almost everyone I've ever seen discussing them on the internet in general. So really, my reason for posting in the mains is because I see no discernible difference in quality, only activity. More activity creates more information requiring more attention, and less activity creates less requiring less.