I just traded cars and have some weird things with the new (used) car. Streaming anything, music or audiobooks, from the phone yielded stuttering output that would mysteriously come and go. It would work perfect one trip and then not at all or mostly the next. I have a Fitbit watch and it occurred to me that perhaps the watch communicating with the phone via bluetooth was to blame. So while the issue was present, I force closed the Fitbit app and immediately the audio stuttering stopped. Anyone else having issues might try shutting down any other apps using bluetooth at the same time as streaming to your car stereo. I have also used the phone in two other cars without any issues, 2013 Audi S5 and 2014 Infiniti QX60 both worked flawlessly. However my 2012 Infiniti M56 has the aforementioned stuttering issue.
Last night I also discovered than if I'm streaming an audiobook via the Audible app, that when I change the car stereo away from the bluetooth source, the app keeps playing the book even though no sound comes out of the phone. Easy enough to mitigate, but I have not had this issue with my other cars. So obviously it's not an issue with the Nexus 6p.