This is interesting point you did Nacher. Recently I was auditioning X-Can(v2) with my HD580 headphones and compared them to the headphone output of my portable CDP Technics SL-XP350 (7 years old). X-Can(v2) amp was connected to portable link output. After few hours of switching from one source to other I concluded that the difference was very small and was exposed only on particular music.
For example I tested Vanessa Mae: The Violin Player that I was not able to distuinguish on any source
(probably due to the techno nature of the sound). On completely different instrumental recording with outstanding (female) vocal, I was able to percieve small difference I would describe as "more open or nature" sound.
After that I have tried (just for curiosity) to audition the same CD on X-CDP X-Can(v2) combo and compared it to X-Can(v2) portable combo. For those two cases I did not find any differences at all. Maybe I was already tired in listening, but in the same time I also tried to audition HD600 from the studio (just for curiosity) and immediately could tell the difference from my HD580, so I was not completely deaf yet
.
Conclusion, I would say that not every portable has to have bad output, and more, I believe that people tend to exaggregate, when describing the difference they hear after they added headphone amp to their portable.
IMHO to significantly improve the sound from headphones like Senn HD580 or HD600 one should invest quite a bit in CDP as well. BTW: Later then I had an opportunity to listen to NAIM CDP with "normal" speakers and it indeed sounded better then my HD580 and Technics portable, but CDPs priced in the USD 300 level, I would say, do not justify USD 250 head amp.