We use a state-of-the-art non-equilibrium quantum transport simulation code, NEMO-1D, to address the device physics and performance benchmarking of cross-plane superlattice Peltier coolers. Our findings show quantitatively how barriers in cross-plane superlattices degrade the electrical performance, i.e. power factor. The performance of an In0.53Ga0.47As/In0.52Al0.48As cross-plane SL Peltier cooler is lower than that of either a bulk In0.53Ga0.47As or bulk In0.52Al0.48As device, mainly due to quantum mechanical effects. We find that a cross-plane SL device has a Seebeck coefficient vs. conductance tradeoff that is no better than that of a bulk device. The effects of tunneling and phase coherence between multi barriers are examined. It is shown that tunneling, SL contacts, and coherency only produce oscillatory behavior of Seebeck coefficient vs. conductance without a significant gain in PF. The overall TE device performance is, therefore, a compromise between the enhanced Seebeck coefficient and degraded conductance.