I like Byobu. Not only can you post something only certain members can see, but you can also just leave your username only, and you've got a private post only you can see. In case you want to make a note for yourself or something.
But, it's in the main forum. I think when people ask for Private Messaging, they want to be able to send another member a quick message in a separate area. Like most social media sites do it. Also, you can have private messages, if done in this way, listed by member. In other words, you can go to your private messages page or pop up and see every member you've had a private conversation with and easily pick that conversation back up at any point. Or, block them. Or delete the conversation.
I don't know which way is better. Part of me likes the way Byobu does it. And part of me likes the instant message type private messages.