Cardboard is more versatile as a stropping substrate for compound. If simply knocking off loose & weakened burrs from an edge, plain cardboard will usually do OK for that, and sometimes it does it very well. If any refinement, thinning or polishing is the goal, that's what the compound (appropriate to steel type) is made to do, when used on cardboard, paper, wood or any number of other substrates able to hold it.
Heavy corrugated cardboard can also sometimes work to straighten or realign a very thin, rolled edge on a blade. I've sometimes used it that manner, to straighten the tip on an extremely thin sheepsfoot blade of mine (Case stockman in CV).
David