I ran some un-scientific tests and found intriguing results: it seems the problem occurs with certain presets but not others.
Keep in mind, in all those, the Playback and Overdub levels were at 100%.
I have recorded myself playing then letting the looper play it back to me.
Then in Photoshop, I overlapped the resulting sound waves from an Audacity screenshot.
Blue area is the live guitar sound, yellow area is the played-back sound.
First riff with the Line6 Dreadnaught preset: pretty much no difference
And here's a different riff with a preset of mine: you can see a notable difference!
I can't pinpoint exactly what factor is the deciding one: my preset has lots of effects (Reverb, echo, Flange) and no amp...
I surmise that, from a certain level and up, some kind of compression is applied.
Anyway, hope this helps someone along the line: if I find a solution, I'll post it here!
Cheers,