I have had this same problem for years. I think it's more a problem with the OS than any one phone. I started with a Motorola Droid and have since moved to the Samsung Galaxy Nexus. I've also changed head sets twice. Always had this choppy audio problem.
I use my phone while I jog, depending on how long I jog it can take 45 minutes to 2 hours. The first 15-30 minutes there is no audio problem, but after 30 minutes the sound begins to cut out. At first it seemed to be a head movement thing, as I would really only notice it if I turned my head. This kind of lead me to think maybe the phone was trying to conserve power by only sending a signal strong enough for where the head set was, and if I moved my head it changed the distance. But the signal drop is to often and to constant for that. Also thought the phone might be flooded with internal signals since I was moving, the gyroscopes and accelerometers might have been flooding the OS with signals even with the screen turned off. But one day I stopped and sat on a bench for 15 minutes after the audio started dropping and it didn't stop dropping.
It's also not a streaming problem. When I run I turn off the Mobile Data, Wi-Fi, NFC and GPS so that I can conserve battery. The Galaxy Nexus is a power hog, and I've lost power several times during really long jogs if I didn't turn those off. All my audio is stored on the phone, and played off the internal storage (no SD card on the nexus). There has to be some problem in how the OS handles Bluetooth.
It doesn't drop as much if I'm not jogging, so something with activity does cause the problem to be more pronounced, but I do find the problem still occurs to a lesser degree if I'm just sitting at my desk at work, it's just not as bad. I don't have this problem with wired headset, so it has to be a problem in Bluetooth. I've also started to notice that if I use Bluetooth all day, the music player stops working and I have to reboot the phone.