I see the Messaging Menu more like a proxy to conversations *and* messaging, the Me Menu would be more of a identity and status panel, representing Me, rather than communication.
The status messages i can "compose" in the MeMenu hardly justify calling it an "outbox".
In the Me Menu Spec¹, something called "Custom Status" is mentioned, which has never been implemented. Althought we have the broadcast field ATM all i wanna believe is that in fact i am seeing that "Custom Status" field, embedded, since i know that from all IM apps i ever used and i find it hard to understand otherwise.
Such an IM status text is not a conversational message, it is a description of "Me", hence aka "status text".
As long as the two menus are not merged, the only one meant for messaging is the Messaging Menu in my eyes. Trimming that one down to its semantic core is a good thing, because that would later on facilitate its integration into another menu, e.g. the Me Menu, that's why i liked what Conscious User did there.. ..not because it polarizes the two menus into IN and OUT.
¹
https://wiki.ubuntu.com/MeMenu#Instant%20messaging%20statuses