I read through Apple's documentation, Bluetooth standards, and Wikipedia articles for different codecs, and I tried to summarize my findings in this post. The post talks about Mac, but it's probably relevant to other OSs as well.
As a disclaimer, I want to state that I've made this investigation for fun, learning, but also profit. I'm working on a Mac app that aims to help with the audio quality when using bluetooth headphones. I decided to work on this project out of frustration, probably shared with more people here, and that's why I'm submitting it.
I hope you find it interesting.