Generally speaking my guess is we're looking to clear out dead root mass, that means eating up cellulose. Cellulose differs from other polysaccharides like starches and glycogen by the type of linkage between monomers. Most starches have an alpha-1-4 linkage, cellulose has a beta-1-4 linkage. A specific enzyme is, thus, required to break it down. This is why cellulose is part of our fiber intake, as we do not have endogenous enzymes to break it down with.
Paper is typically made up of cellulose pulp, so for that reason I'm inclined to go with the shit that's eating up the paper. But enzymes have different efficiencies under different circumstances--temperature, wetness/dryness, accessible surface area of material, and so on. In practice the best thing to do is set up some dixie cups, grow some roots out, and then kill them. Watering them as you normally would, keeping them where you normally would--and then observe the results periodically. It would help immensely if you had a way to visualize the root zone while the breakdown was occuring (or a way to see progress without disrupting the soil). For instance, if you were to do this same experiment in a pot with a plexiglass cross section (ie 1 half of a pot affixed to plexiglass that you can put in darkness so as to not disturb root growth, but uncover when you want to see what's happening)--you could take pictures in a standardized way, take measurements, and really get some good data.
Then, ultimately, do the same thing in larger pots to confirm your results.
By then my guess is you'll have a clear winner in hand. It may be that the one that eats through the paper is the best (and if I had to hypothesize, that would be my guess)--but if you actually do the proper testing you'll know rather than think.
Just to clarify, you're doing a similar experiment as the video here--you're just doing it under your real conditions. The real model often deviates from the ideal model when its put to the test, and that's why it's important to do this. Its because *similar* isn't *same*--and a cup filled with liquid and paper isn't the same as a pot filled with soil and roots.