Here's the thing about the AK Amp - I really don't think its output is as clean as the one directly off the AK380. With sensitive IEMs, it produces a mild hiss and it's audible enough for me to know it's there. I am unfortunately one of those people who are extremely sensitive to hiss. I never use the amp module unless I'm driving less sensitive / demanding headphones. For line driving purposes, the output directly off the AK380 is just perfect. It measures remarkably well and there is no hiss whatsoever even when using the most sensitive of IEMs and this I appreciate very much.
The hiss on the amp module is a weird one. If you enable the amp without playing anything, there is no hiss. It's dead quiet. It's only when you start playing a song that the hiss becomes noticeable. So, you need to test this with some tracks that has a fair bit of quiet passages. When you stop the song, the hiss goes away. If I use the amp module as a line driver to drive another amp, the hiss, unfortunately also becomes part of the signal and that is a huge, huge deal breaker for me regardless of how good it may sound (I honestly didn't think it sounded any better than directly off the AK380). Line driving directly off the AK380, no such issues and that is why I never use the amp module unless I need to desperately drive either my LCD-3 or HD650 on-the-go. And I say desperate because the AK amp drives both cans less than satisfactory, even at high gain, single ended or balanced regardless. There's enough headroom but it doesn't have the bite, the punch and there is just no finesse of any sort.
My personal take is - the AK amp leaves me wanting and because of that, it's almost always in the storage box.