If that Teac had output designed following proper electric engineering for its price there wouldn't be much of possiblity for real audible differences from separate amplifier in non-biased blind testing.
Except for tubes/valves which aren't neutral/transparent and have real effect to sound.
But it seems to have been designed using some ancient standards with over 100 ohm output impedance...
Possibly using output resistor also as cheap and dirty short circuit protection and/or to keep amplifier stable with reactance of some headphones.
http://reference-audio-analyzer.pro/en/report/amp/teac-ud-h-01.php
Amplifiers for speakers can also have headphone output simply connected to speaker output using resistors instead of having separate headphone amplifier.
Interaction with it is going to have effect to frequency response of non-flat impedance curve headphones.
HD650 have higher base impedance, so effect isn't that huge unlike it would be for low impedance HD598s:
http://graphs.headphone.com/graphCompare.php?graphType=7&graphID[]=853&graphID[]=2851&scale=30
With HD598's only 1/3 of output power would drive headphones at most frequencies...
But at driver's resonance frequency that would rise to almost over 2/3 boosting bass lot.
Besides frequency response output impedance has also effect to damping factor which tells how tightly driver's movement is controlled by voltage source.
For technically "close enough to perfect" control headphone impedance should be at least ~8 times output impedance.
With damping factor decreasing headphone's drivers start gradually following signal less and less tightly with their own natural vibrations starting to show up.
Thanks to HD650's highish impedance that's not much of problem in this case.
When and how much effect of decreased damping factor appears likely depends on headphones.
But at some point sound eventually turns to total mess and bass loses all of its power.
