iPod Touch 5 vs iPhone 5s sound output (Line Out)
That is very weird; do you have a European version?  The output power on those is heavily limited. That is the only explanation. 

I have both the iPhone 5s and the iPod touch five and they have the exact same output voltages and voltage drop when headphones are connected. The output power is the same, I have heard from a few sources that the distortion levels on the 5s is better but they definitely have the same output level. Be sure to verify that the equalizer is disabled and sound check is off