In this paper, the abilities of injected current magnetic resonance electrical impedance tomography (MREIT) and induced current magnetic resonance electrical impedance tomography (ICMREIT) systems to differentiate a conductivity perturbation from an otherwise uniform conductivity distribution are compared. The sensitivity of MREIT measurements changes as a function of distance to the electrodes used for current injection. The sensitivity of ICMREIT measurements is related to the radial location, being a minimum for concentrically located small conductivity perturbations. The very low sensitivity of ICMREIT to conductivity perturbations at central locations seems to be the major drawback of the method compared with MREIT. When the diameter of a concentric and/or an eccentric circular conductivity inhomogeneity inside an otherwise homogeneous circular conductor is close to half of the diameter of the conductor region, the distinguishability of the perturbation by MREIT increases. MREIT is more sensitive to perturbations with lower conductivity with respect to background conductivity (resistive perturbations) than to conductive perturbations. In the case of ICMREIT, concentric inhomogeneities are equally distinguishable for conductive and resistive conductivity perturbations. Eccentric resistive inhomogeneities are more distinguishable then conductive inhomogeneities. Distinguishability increases with the size and number of conductivity perturbations.