Combining DNA origami with solid-state nanopores has been gaining an increasing amount of attention due to its potential for biosensing applications. Accordingly, origami plate dockings onto conventional solid-state silicon nitride pores with membranes of ?20nm thick were previously studied. Here, we examine whether graphene, with its single layer of carbon atoms, poses advantages over silicon-nitride pores. The conductance blockades due to origami plate dockings were characterized as a function of salt concentration and applied bias voltage and compared to the silicon-nitride data. As expected, it was found that conductance blockades increase with salt concentration and voltage. The relative conductance drop in graphene was however found to be similar to that for silicon nitride pores, whereas theory predicts that the blockade signal is larger in graphene pores. We have further compared the root-mean-squared noise levels of the ionic current through hybrid graphene-origami pores and bare pores, and found that the noise in the hybrid pores was slightly higher than in the bare pore current. Finally, it was tested whether the plates stick to the graphene pore in presence of EDTA. This was done by docking the plates and subjecting them to a negative ramping voltage. Without EDTA, no evidence of sticking was found, whereas with EDTA, 88.2\% of docked plates appeared to be sticking.