There have been people before who said they liked the 4v sound output better.
Sure, if you define "sound quality" as "louder". The home outputs should deliver the same sound quality as the car outputs do, just at a different voltage.
I would really like to know his definition of "sound quality". He could be referring to many things, volume being one of them. He might mean that he's got ground loop noise on his home stereo. He might mean there's not enough bass. He might mean that his home stereo is better and lets him hear the MP3 compression artifacts more clearly. He might mean he's getting distortion because he plugged the player into the "phono" jacks on his home stereo (a no-no). He could mean anything. So let's see what his definition of "sound quality" is, first, then we'll work on the problem.