I'm new to headphones and high quality music, and I kinda leaped up to the Grado ps1000 headphones because they sounded best to me. Ive been listening to them right out of the headphone jack of my asus essence stx soundcard for over a month now, and they sound excellent. However, been trying all kinds of things out at a friends house. Regrettably, he only has one amp (woo wa22) so I cant test this too much, but, I have listened to my headphones through the headphone jack (which will drive even lower efficiency), from the wa22 using the sound card as a dac and hooking it up rca analog to the wa22, and using the digital optical out of the computer to several different dac's, and I can tell the difference. Although, admittedly the wa22 is a tube amp and the asus stx is solid state, and those were my only 2 options. However, I definitely noticed a very distinct difference particularly going from amping from the stx and to the wa22. I could also tell the difference between the dacs, but admittedly most were very small, mostly a difference in soundstage and bass were the only two characteristics that were the most distinguishable. However, the quality of the bass was very easy to tell, especially as my new headphones are new, they have had a very bloomy bass right out of the stx, and it has been clearing up, but put it on the wa22, and its gone, and left with absolute precise bass, and I can tell when its deeper bass and when its mid bass as well.
Now...whether there is a difference from high dollar amps and mid grade, I do not know... but for my headphones, there was a very noticeable difference (and I can do it blind, and from the next room, next day, whatever test you want to throw at it.
Now if my headphones break in with a tighter bass, then it might be a bit harder to tell, but the fact that there was a difference should be telling enough