I use both all around my property. Newspaper die is soy-based. The earthworms love to crawl between the cardboard, and both breakdown quickly.
I don't know what the organic people would say though. I never use any pesticides or purchase any fertilizers. Everything comes from
compost, worm castings, leafmold etc...
Deep mulching, hand picking and predator species also contribute a lot.
We are happy with our organic approach. May be more rules in selling organic certified produce though.