is the loudness of the music being played determined by the CD player, or the headphones? i have never used a portable CD player so i can't really answer this one, any help would be appreciated.
As with a typical amplifier and speakers, the same holds true for your combination. Headphones have varying sensitivity specs which will produce different volume levels with the same amount of power. Headphones also have varying impedance loads to show the amplifier. The output chips in the players have minimally greater or lesser amounts of power available and the maximum power output is determined by when the amplifier can no longer produce clean power, i.e. clipping.