We demonstrate numerically that the theoretical maximum sensitivity of a ring-coupled Mach-Zehnder interferometer (MZI) optimized as a sensor is about 30% greater than the optimized sensitivity of a conventional single-bus ring sensor with an identical ring perimeter and loss. The ring-coupled MZI sensor also achieves its greater sensitivity with a 25% lower circulating power, which is useful for the suppression of undesirable nonlinear effects.