Can I ask you to explain? I do not have any knowledge on how it works... Why do you think the sound out of integrated could be something that I prefered over NFB-11? I actually do have a good integrated British stereo amp at home and a few times I tried it with headphones I really liked how it sounded. So you must be on to something. Can you please explain and also how do I get that sound with a computer desktop setup?
Integrated amps have a tendency to have a high output impedance on the headphone output. When you have a high output impedance and you put a headphone on it, it has an EQ effect on the sound.
If you're putting a higher impedance headphone on it - roughly 150ohms and up - you'll get a boost in the midrange. This is partly why a lot of people like using OTL amps on 300ohm Sennheisers, the other being that since such amps are biased for delivering a lot of clean power at high impedance, they're not getting more noise nor the bad kind of distortion much less clipping vs a similarly lower tier solid state amp.
When you put a lower impedance headphone, you get an EQ effect in two ways. Either it trims the bass or boosts it, although tendency is that either way the bass lacks refinement where fast individual notes can get blurred. In some music this isn't crucial, unlike, say, metal. In other music getting that boost adds the "kick," without the blurring bass lines or double peds that you'd get on music with very fast bass notes.
Basically, what you're after is a subjective effect, not something objective where we an easily list amps that will not alter the signal as it drives the headphone, so you can hear the music as the headphone really sounds like even at high volume. Note that while that may not necessarily be the same as Diamond Audio's "Just Like The Artist Intended" (which is actually a problem, since all speakers/headphones have coloration, and you'd have to use the same monitors the albums are mastered on or the same hi-fi speakers they tried it on after mastering), having the upstream components EQ-ing the sound isn't necessarily any closer since you're basically EQ-ing at random rather than just flattening out peaks in the headphone/speaker response to get closer to a flat response.
You could try a headphone amp with a relatively high output impedance but the problem with this is that you're gambling on it boosting than the opposite. There's a way to predict which one but you need a lot of the specs on the headphones and the amp, so basically chances are you'd still end up just gambling.
Or you can try a really powerful headphone amp and listen a bit louder, with a headphone amp that has a lot of both voltage and current, like Violectric, Lyr2, or Burson. The Burson at least runs Class A, and from what I've heard from their more powerful amps like the Soloist and Conductor, compared to an O2 which is a bit sharper and barely has punch and a Meier which is more rolled off and is punchier than the O2, the Bursons are really going to pound your head with strong bass notes without sacrificing how well the bass notes don't blur in faster music. On the Lyr2 you can try different preamp tubes. VIolectric (and also Meier amps) aren't as punchy as Bursons but it's not like they really don't have any punch - they have more than the O2 which has sharper treble reproduction when pushed which detracts from your hearing the kick of the low end (ie it's there, you're just getting distracted by the treble) on top of which these amps (O2 and Meier included) have ridiculously low noise floors, so you don't have any noise getting in the way of the low end.
