In many cases, you need not go through this process, as valdikss now keeps track for many of the contributed results on his website
If you have trouble finding your btsnoop_hci.log file, please try solution posted here:
Once you find your btsnoop_hci.log, please start at step 7 in the Previous Answer below.
[Credit for this answer mostly goes to ewedel, who clarified that the answer is in the btsnoop_hci.log file, using Wireshark; and prittstift69, for sharing the easy way to create this log file.]
This is a newbie-friendly, step-by-step tutorial, summarizing answers already given, with some interpretation of the results from me.
As prittstift69 and others mentioned, you can "Enable Bluetooth HCI snoop log" under Developer options. No need to follow the more complicated approach suggested by ewedel.
Start by turning bluetooth OFF on the android device (I'll call it 'phone').
Turn on Bluetooth HCI snoop log under Developer Options.
Turn ON Bluetooth on the phone and connect it to the Bluetooth receiver (I'll call it 'receiver'). This step assumes that the receiver had been previously paired with the phone.
Play music on your phone (ideally an uncompressed WAV or FLAC file). Ten seconds is all you need. (Probably even less)
Turn OFF Bluetooth on the phone.
Turn OFF Bluetooth HCI snoop log
Transfer the file btsnoop_hci.log (I found it in /sdcard/Android/Data/) to your computer. Run wireshark on your computer and open the file btsnoop_hci.log
Filter for "btavdtp" (no quotes) Search for a message from the phone to the receiver "Sent Command - SetConfiguration ...." This is the message sent by the phone to the receiver with the final configuration to be used for this audio after the handshaking is completed. The text in the Info field will tell you what the final configuration was.
[SBC] If it is SBC, you may want to know what the bitpool is. To do this, remove the Filter for btavdtp and look for a message with Protocol SBC and click on it. Below, in the details section, expand the Bluetooth SBC Codec information. Then expand any (or all) of the Frame data. There, it should clearly show the Bitpool used by that Frame. If it is 35, there is a good chance that your sample rate is 44.1 kHz, you are using Joint Stereo, and using the Middle Quality SBC audio profile (http://soundexpert.org/news/-/blogs/bluetooth-audio-quality-a2dp). The bitrate for the compressed audio is then 229 kbits/sec SBC, which scores a 4.68 in Sound Expert's testing (http://soundexpert.org/encoders-224-kbps) which is comparable to mp3 around 110-130 kbits/sec.
[APT-X] If it is APT-X, then both your phone and receiver support APT-X, and that is what it is using. Assuming 16-bit, 44.1kHz, the codec is running at 352kbits/s.