If the cardboard and plywood are of similar total thicknesses, the cardboard should cut much easier than the plywood - BUT! - with more smoke and a greater chance of flames. This is because the cardboard is much, much thinner in each corrugation, and the air between each corrugation will let the hot "paper thin" cardboard get oxygen to burn once it reaches "char" temperature. The plywood is much denser, has no holes or vent paths, and so does not heat up locally as much.
BOTH the cut-off remnant falling towards the scrap heap AND the product left on the table will be hot enough to burn, smolder, and to potentially catch fire later in the pile in the corner, or the stack left in the rack. Consider a cooling flow of CO2 as well, plus a CO2 flood capacity in the room. And in the trash pile/trash bin.