Apparently the S3 audio quality is fairly decent. Nothing spectacular, but it's decent. I know a couple people with the phone.
You should look for phones with Beats audio built in. They have a separate circuit on the mainboard for the audio, which reduces electrical interference and therefor improves sound quality. Some of them even have very small, built in amplifiers for high end headphones. A lot of HTC phones have this feature.
sounds good but i'm not so sure i would trust anything associated with "beats audio" as the headphones are complete garbage.
unless you're a complete audiophile "good" audio quality is likely going to be fine.
i had some $180 headphones hooked up to my incredible 1 streaming some 192/256kbps internet radio or mp3 files and it was fine. perhaps someone else may find it lacking but so be it. sorry i cant comment exactly on your model since i dont have it.
an external amp such as a fiio would be much better than an integrated amp.