Coupled oscillator arrays (COAs) can be used to control the phase distribution across the aperture of an array antenna in such a manner as to affect steering of the beam without the use of phase shifters. Given the various possible planar configurations of COAs, a systematic design approach is necessary. In this study, the authors present a comprehensive comparison of various configurations of planar COAs based on their sensitivity to random errors in their free running frequencies. The parameters considered are (a) the beam pointing error of the array, (b) the locking probability, (c) the side lobe level, and (d) the beam width of the radiation pattern. These results can serve as a design strategy for choosing optimal configurations of planar COAs based on the needs of each particular application.