If you have a personal issue with someone, where you are both on equal standing then you should keep it in private unless you believe that the person poses a risk to other members. By all means talk to your friends in PM about the issue, that's fine if you want to do that. I'm not a fan of public assassinations unless the target has clearly asked for it, by which I mean that they've willingly transgressed in a manner that is utterly cruel or inappropriate. This does not mean that they've disagreed with you. This means that they've harrassed you or bullied you, sexually or otherwise, or they're acting illegally. Obviously the correct course of action according to the TOS would be to block or report, or both, but I wouldn't blame someone for going public in these instances.
