My general preference is for threaded rather than flat comments. If you want to dive into a particular aspect of a topic in depth, they allow for this.

I've seen flat discussion style particularly on G+. While I strongly feel it doesn't scale well, what you do get for small discussions is a conversation which feels a bit more like a handful of people talking in a room. Assuming people are clueful enough to read the preceding comments and take them into account (observed more in the breech), there's more of a chance for side conversations to work their way back into the main stream.

The problem is that, as with a discussion in a room, the discussion tends not to scale well. Past a half-dozen to a dozen primary participants, continuity tends to be lost. Threading allows for break-outs of specific interest. Sites such as reddit (with RES) that allow expanding or collapsing of specific sub-threads (RES's "hide all child comments" is great for busy posts) are particularly useful. I find that navigating reddit threads on busy posts to be somewhat challenging: too many open/close options and long threads are cut off too soon, particularly when you're viewing just that thread.

HN wants badly for a specific "response to comment / post" feature. You can view your threads but have to find and respond individually, and responses to anything but recent comments get lost.