It is known that ionic liquids (ILs) assemble differently at an electrode surface compared to traditional electrolytes; however, the impact of this on electrochemical processes is not yet clear. In this work, we investigate interfacial behavior of two ILs, 1-ethyl-3-methylimidazolium dicyanamide ([C2mim][dca]) and N-butyl-N-methylpyrrolidinium dicyanamide ([C4mpyr][dca]) in the context of a rechargeable zinc battery. In previous experiments, [C2mim][dca] outperformed [C4mpyr][dca] in several ways (e.g., lower overpotential required to initiate electrodeposition of zinc, higher zinc deposition peak current density, and greater number of supported charge-discharge cycles). Here, using molecular-dynamics simulations, we investigate a set of mixtures containing zinc in those ILs, confined by graphene electrodes. Our results reveal the presence of layers and show how the two systems differ with respect to those layers: [C4mpyr][dca] exhibits a tendency for high overscreening and undergoes a transition into the crowding regime, whereas [C2mim][dca] exhibits low overscreening and shows no signs of crowding. As a result, the interfacial concentration of zinc and anions is higher in [C2mim][dca], strongly suggesting a large impact on the electrochemical performance of a battery.