it's not about loudness.
it's about control.
i had my d4 paired up with only a 250 ohm dt880 for a while.
and i thought it sounded pretty good, too.
however, i just found myself pulling the headphones off after a few songs.
and finally realized my ears were getting fatigued. and i don't really listen loud.
what i was hearing, or rather not hearing consciously, was the noise floor.
the d4 is an impressive little unit, but really only good for low impedance cans. i have it paired with my m50 now, and i love the combo.
but the 600 ohm beyers, they need dedicated wall-powered amplification.
the udac, d4, and others mentioned - those run off phantom power from the usb cable.
for 200 bucks, you can get an audinst hud mx-1, or an audio-gd sparrow, or a few other options that plug into the wall, and also have a dac.
i would, however, avoid the hifiman ef2a.