Should Inter-Jelly disputes be conducted within a thread or via PM? Or when should one choose one over the other?

This question started out being an attempt at a PM apology to a fellow jelly who got an earful from me after tossing out a rather baiting (IMO) comment that pushed my button. For better or worse, I decided I was not so much feeling apologetic as being able to better articulate a difference of opinion in my cooled off state.

The opinion is that I have long favored settling my disputes with other jellies publicly and within a thread. I think it keeps communication honest, minimizes potential for verbally abusive comments, allows for moderation of abusive comments, and, most importantly, allows everyone to assess the credibility of the individual jellies in dispute. I was surprised, then, to find myself trading barbs with someone who more or less thought that I should have had enough sense and decorum to relegate the argument to PM. This person was of the opinion that I should have communicated my problem with them directly.

To add a layer of complexity and disclosure, the above exchange was precipitated by a thread comprised of helpful and unhelpful answers (although they were not unhelpful enough to be removed by moderators). I contributed an unhelpful answer (but also felt there were plenty of helpful answers).

What say you and why?