I have always preferred using military time because there is no confusion of AM or PM. When writing it in report its also easier, because there is less to write. For example I could say at "The suspect entered the building at approximately 7:45 AM." Or I could say "The suspect entered the building at approximately 0745 hours." When you use military time, there is no need to specify AM or PM. It explains itself. There is also no need for a colon when using military time.
I also keep my watch set to military time. However, if some asks me what time it is, I always tell time using AM or PM. I think most people don't like it because they don't know how to use it. Its very simple. Anytime the hour is 13 or more, just subtract 12 from it. If military time shows 1500 hours & you subtract 12 from it, then you'll know that it is 3:00 PM