The cardboard sword is preferable because the term can apply to swords made out of a range of hard paper products.
Corrugated fiberboard swords can cause a world of pain when used against someone's eyes. I wouldn't be screaming pathetic if I got jabbed in there with one.
I think I would just turn the feather around and use the sharp end to impale the person weilding the cardboard sword. If there is no human involvment I would bet the cradboard would win since it dosen't seem as fragile, unless the feather had complete control of itself then the cardboard would lose because it would prolly be too stiff to move quickly. Either way I'll have my camera out recording this fight.
I set them both on fire to make it intresting! Then i throw some magic words and rune's around...and i wouldnt be suprised if the animated feather sword won!