Owing to quite different features and hysteretic behavior of friction pendulum bearings (FPBs) and sloped rolling-type bearings (SRBs), their control performances might not be readily compared without some rules. In this study, first, on the premise of retaining the same horizontal acceleration control performance, the effects arising from different sloping angles and damping forces on the horizontal maximum and residual displacement responses of SRBs are numerically examined. For objective comparison of passive control performances of FPBs and SRBs, then, some criteria are considered to design FPBs with the same horizontal acceleration control performance by referring to the designed damping force and the maximum horizontal displacement response of SRBs under a given seismic demand. Based on the considered criteria, the passive control performances of FPBs and SRBs under a large number of far-field and pulse-like near-fault ground motions are quantitatively compared. The numerical comparison results indicate that the FPB models might potentially have better horizontal acceleration and isolation displacement control performances than the SRB models regardless of whether they are subjected to far-field or near-fault ground motions, while the opposite tendency is observed for their self-centering performances, especially when the SRB model designed with a larger sloping angle or a smaller damping force.