I have a JVC head unit that used to display a box saying I had a new message and play a small tone. After the Kit Kat upgrade, this feature is absent. I feel it has to do the the Bluetooth MAP (Message Access Protocol) that Google made standard in Android 4.4, and that it does not play nicely because of the notification listening service that all devices running Android 4.3 use. My theory is that without an actual app, the phone can no longer send (or receive, in your case) information about messages. The problem with this is simply that while you are connected to Bluetooth, Android doesn't recognize that it is supposed to send information about your texts to the head unit.
So, the theory I have is that if the head unit had an actual app for Android that allowed for the head unit to actually read the messages through the notification listener service, then this feature will return. After reading this I remembered there was an Android app from JVC/Kenwood that allowed the control of the head unit through your phone. The JVC version is "JVC Smart Music Control". There's a Kenwood version called "Kenwood Music". Try installing that and see if it helps. I just installed the JVC version and hopefully that helps, although its sad that now I need another app to do something that happened before. Not that I mind that much, but without any information about why this happened it makes it difficult to understand.
Oh, and don't text and drive. Haha.