Did you ever get an answer to your question? I have noticed the same thing. I just upgraded from an Intenstiy I to an Intensity III and all the messages go into one "bucket" instead of being seperated by "Received", "Sent", and "Drafts". It makes it more difficult to organized and find messages.
I did get an answer. I actually found it from what someone wrote in reference to the Intensity I, but it is the same with the Intensity III. Under the "Messaging" menu, select "Settings" , and then "Inbox View". There is a choice for "Time" or "Contact". If you set for "Time", then the messages menu will show the choices of "New Message", "Inbox", "Emergency Alerts" (new to the III, i guess) " "Sent", etc.
Let me know if that helps.