The one downside of threading is that it encourages people to spin off conversations and splinter discussion into a myriad of subthreads. That's appropriate for a discussion board, but if there's an option to take the conversation private (e.g. email), I'm less convinced that threading should be supported, as any remaining comments should be germane to the original subject. Admittedly, this results in the hacks like Twitter of doing @person to indicate who you are responding to.

I guess the question is, are the comments meant to enable communication among the commenters, or to provide feedback on an original piece (a news story or blog post). If the former, then threading. If the latter, maybe not.