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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As primo said, I also enjoy the company of someone else's opinion on a subject, even if it isn't the same as mine. The mains are good for chatting with lots of people. [Edited on 01.02.2013 12:58 PM PST]