Falsetto utilizes "false" chords in the larynx, which is why its called "Falsetto."
My Best way to explain how falsetto sounds verses full voice is go listen to Jim Gaffigan do his skit, whenever he does this high voice thing, hes using falsetto, falsetto in my understanding is always very soft. If someone is singing full voice and very loud, then they go to hit a quiet high note, they are using falsetto.
As a singer very similar to Nils, I can attest that his voice sounds very "full" when singing, and I don't really hear him using Falsetto very much.
Hope this answers your question!