As far as audio quality is concerned, there are no advantages. The advantage is the ability to not have to run any audio cables to get your digital audio in and out of your AJA IO or Digital VTR. Embedded SDI Audio was developed so that broadcasters could have large SDI routing switchers that could handle all the digital audio, without doing any AES wiring. You can see the advantage of this if you have many edit systems, and many Digi Beta, Beta SX VTR's, and with a single inexpensive SDI router, you can not only route your digital video, but your audio as well, with a fraction of the labor and parts involved.
When you have a single AJA IO box, and a Single Digi Beta VTR (like a Sony J30SDI for example), you just need ONE BNC CABLE to get all the multichannel audio into the AJA, simply by selecting embedded audio. The AJA will de embed the audio for monitoring.