At least cardboard decomposes, whereas plastic remains in a landfill for eternity.
BTW, landfills aren't great environments for decomposition even for paper and cardboard - the weight and compression make for a hostile environment for aerobic microbes and for the larger animals (rodents, insects, worms) that usually help with the first round of decomposition and increasing the surface area available to the microbes. If you dig into a landfill, you can often find 75-year-old newspapers (made of some of the least durable materials around) completely intact.
Mid-to-late 20thC landfills are the worst of all because there's so much plastic and styrofoam, the ratio of decomposable materials is very low.