I would assume both. Overcompressing down or synthetic would surely damage fibers. And most materials loose form when kept under tension for a long time. I think down is a bit more resistant to this than the current synthetics, though.
Nonetheless, I would not compress my down gear for long times if not absolutely necessary. Get a big bag and simply store the quilts next to your pack. It only takes 5 more minutes to stuff the quilts into the backpack.
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