My gues is that your jawbone headset is not compatible with the A2DP profile. Which is a pretty standard profile for streaming high quality audio via bluetooth. That would explain why it would work with your other headset.
This is common since handsfree type headsets are usually mono with a microphone. There are designed for communication, not streaming high quality audio.
I have noticed the same thing. My phone wouldnt play music and such on my Jabra handsfree but will over my in car pioneer deck. Same goes for the Nav voice and other audio notification services like vlingo. When a researched it, that is what I cam up with, and it made scence for me. So unfortunatly, we are out of luck on that one, it has nothing to do with the phone, its the design of the headsets.