Although solid electrolyte ceramics based on stabilized ZrO2 are widely used for various high-temperature electrochemical applications for many decades, there still exist a number of important challenges associated with long-range ordering and degradation processes, phase separation and grain-boundary blocking phenomena, and microscopic mechanisms of interfacial reactions and transport in the intermediate-temperature range. In order to assess the relevance of grain boundary-related factors in ZrO2-based membranes for the performance of solid oxide fuel cells (SOFCs), the present work is centered on comparative analysis of the ionic conductivity and long-time stability of a series of ceramic and single-crystal zirconia membranes. Primary attention was given to the ZrO2-Y2O3, ZrO2-Sc2O3-Y2O3 and ZrO2-Sc2O3-CeO2 systems where high-conductivity cubic phases with relatively good stability at the SOFC operation temperatures are known. For the sake of comparison, several commercial powders were used to fabricate dense ceramic membranes, then also tested by the impedance spectroscopy, X-ray diffraction (XRD), scanning and transmission electron microscopy (SEM/TEM), selected-area electron diffraction (SAED) and other methods. The results revealed, in particular, no conductiity degradation for either ceramic or single-crystal membranes of cubic ZrO2 co-stabilized by 10 mol.% Sc2O3 and 1 mol.% Y2O3, provided that the purity of starting powders used for ceramic processing is sufficient. Testing of model SOFCs with polycrystalline and single-crystal electrolytes showed quite similar performance, confirming neglible grain-boundary effects under the fuel cell operation conditions, in accordance with the impedance spectroscopy results.