A music box can play notes, but not audio. You can’t record into a music box, and a music box can’t play a voice, or a violin, or a trumpet. It’s an instrument that plays a pre-set melody, not a means of storing audio information.
A phonograph, on the other hand, can record and play back audio. You can record a voice, a violin, a trumpet, or any other sound.
If your sole objective is to store a short melody that can be listened to, and factors other than the notes themselves are irrelevant (timbre, volume, etc), a music box may be more accurate. If you want to store a piece of audio (such as a voice), that cannot be represented adequately/at all with a sequence of notes, a phonograph is infinitely more accurate.
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