OK, so for posterity (and for anyone who is interested), I have spent a lot of time researching this and have recently found some good info.
The best site I have found for discovering the audio performance of phones is
http://www.gsmarena.com/. If they do a full review, they use Rightmark audio analyzer using the following setup and settings:
http://www.gsmarena.com/latest_features-review-171p2.phpUnfortunately, they don't list all of the audio test results in one place. You need to search for your phone and go to the specifications page. If it's been tested, you'll see an entry at the bottom labeled 'Audio Quality'. Click on the value in the column to the right to read the full set of results!
By going through their reviews, I was able to discover which phones delivered the best audio quality. Note that not all phones get tested for sound quality, so I'm only commenting on what is available that I've checked out. Here is what I've learned:
If you have an iphone, you're basically all set as Apple uses great audio hardware (especially the 4).
However, if you're interested in Android phones, then you will want to find a phone which uses a good audio chip. Wolfson made chips seem to deliver the best quality (specifically the WM8994, WM1811 and WM5102, but there are probably others). There is a kernel patch which can deliver even better audio performance from these chips by tapping in to their full potential at the hardware level. If you're not in to hacking android kernels, the patch is available in the form of an app called Voodoo Sound:
https://play.google.com/store/apps/details?id=org.projectvoodoo.controlapp&hl=enHe lists all the known devices with the supported chips on that page, but this is a free app and you can use it first to see if you have supported hardware. He also has a pay app with more features (it says that if it doesn't work on your hardware, you can contact him for a refund):
https://play.google.com/store/apps/details?id=org.projectvoodoo.controlappdonate&hl=enIf any of you have one of the supported devices, and you decide to try the app, please check it out and let me know what you think. I'll add more to this thread as I learn more.