I don't know all the amps in the world but the most possible case with warmness/brightness is that the manufacturer just designed them to sound this way. For example simple Fiio E11 has emphasis on bass even though you are not using bass switch on it. Fiio E9 is for sure more neutral but lacks transparency. Xonar Essence ST is behaving strange with higher gain settings, being too much distorted... Tube amps are also the case with their harmonic distortion.
Another thing is suitability... Low impedance phones require a lot of current which not every amplifier is able to deliver. Also, amps' outputs are very often of higher impedance than ideal which can cause muddiness in bass and higher level of overal distortion with some phones.
Also, if you do not use ideal gain resistors for every particular headphone, you are loosing transparency and adding distortion. An ideal gain for one pair of headphones is the one where you get loud enough + little more on full volume. Good amp needs to be audibly transparent even when turning the volume knob towards the max.
Stability also plays role... Majority of amps could have good measurements but are starting to perform worse in special conditions (for example with low impedance phones as mentioned before). Also, they are phones which have stable impedance across the frequency spectrum, and there are ones with more diverse graphs (see Sennheisers). This can of course cause problems... Amps powered by batteries are also going to perform weaker in certain categories.
I am sure enough I didn't mentioned all the options that can happen... But the simple outcome from all of this would be that you should only use transparent, neutral and stable performing amp to achieve the best results (read working as it should).
Interesting to read. Thank you for writing such an informative post! I'm starting to get into amps a little bit. I've always kind of tried to avoid tube amps because of their "unclean" signal, but in concept, they are extremely neat to me. I would actually like to get my hands on a Bottlehead S.E.X. or Crack some day just because I think tube amps are so awesome.
I just purchased an Objective2 amp because I've read that it's supposed to be a very good amp for the price. It certainly sounds very good to me and I'm liking the clean, transparent output it has.
One question, though I hope not to derail the thread, how does an amp increase the soundstage? The O2 adds very little colouration, if at all, when connected to my Sansa Clip Zip (yeah yeah, double amplification is a concern in this situation), at least to my ears. On the other hand, the soundstage and instrumentation separation seems to be increased, and I notice this effect too when I connect it to my MacBook (yeah yeah not the best source either).