Yeah, it really depends on *how* you use your device to listen to music. I use Google's app because I actually use their service and have a decent portion of my music library on Google Play Music. If you're just using it to play files downloaded to your device, it really doesn't matter I'd think, you could use either one of those players, or as epidenimus suggested, install a different one altogether...personal preference.
My guess is that there are 2 builtin with the stock device because Google Play music was still in it's infancy when the S3 was being developed, and at the time it was standard practice for OEMs to include their own music player (because the Google one didn't exist). They may actually still be doing this, I'm not sure, but probably not as necessary any more since Google's music player now gets installed by default with the other Google apps.