I almost always listen to music at home, with my opened full size can. I take the IE80s out 5-6 times a year, when I travel somewhere. Never used them with an external portable headphone amp (source is Fiio X3ii). This time (going abroad for a week) I decided to take my iFi Nano iCan, even though it is bulky, and not comfortable to carry around. The sound is just so much better. It is worth the hassle. It lifts the IE80s to the next level.
Bigger space and soundstage, sometimes it feels like certain sound effects are coming from behind your ears. After the space the second most noticable improvement is in the bass section. Feels much cleaner, and definitely goes lower, The sub-bass is much more present, however still in balance with the rest of the frequencies. Mid-bass and higher bass is tamed, cleared down, equal partners of the delightful sub-bass. And all of this with losing nothing in the mid or high region. Just gaining more space and clarity. (With X-Bass and 3D function on). A more fun, more balanced sound. Never thought, IE80 can be improved this much with an amp. (Compared to Fiio X3ii hp out, using custom tips.) I am ready to take the hassle of carrying around a bulky mini hi-fi system, if the sound is this much better.
The only thing sweeps away this portable music experience is my Fidelio X2 from the same player and amp. Getting back to my home rig after 8 days of the above mentioned portability is just another world.
A good amp puts IE80 on another level.
[But X2 takes you to a different world, not just changing levels...]