Line out is a certain voltage level driven for the high impedance inputs of the amplifier. The idea is to maintain the output signal around a certain voltage level. There is not much current being supplied, since this is taken care of by the amp.
The headphone output is driving the headphones, which is a load that requires high current.
The loudness of the phones is actually dependent on the match between the jack impedance and the headphones' impedance (thevenin). Largest power output occurs when the source and load impedances are equal.
An example:
I have a CDP with headphone and lineout jacks. The volume setting affects the headphone jack and not the lineout.
When I use my Grados, and adjust the headphone volume so that the volume I get from the headphone jack is same as the one I get by connecting the cans to the lineout (NO AMP, just lineout), the volume is set quite low.
It is the opposite with the HD-600. The lineout is quite loud with them and the volume setting of the headphone jack needs to be high to match that loudness.
The reason for this is the difference in the impedances. The Grados are 32ohms. They will sound loudest when the source impedance is also 32ohms.
The Senns are 300 ohms. They will sound loudest with a source impedance of 300 ohms.
The headphone out jack has a low impedance (dunno exactly but surely lower than 50ohms) whereas the lineout impedance is high (because the inputs of the amplifier are also high impedance and the signal is not driving a big load like the headphones, but is supplying a signal to be further amplified). This translates to the lineout being a better match for the HD-600 with its high impedance than the Grados with their low impedance.
Your amp is high impedance, and the power output of the system (player + amp) is greater when connected to the high impedance lineout than the low impedance headphone jack.
Hope I am clear enough and am actually answering your question.