The entropy at the output of a quantizer is equal to the average mutual information between unquantized and quantized random variables. Thus, for a fixed number of quantization levels, output entropy is a reasonable information-theoretic criterion of quantizer fidelity. It is shown that, for a class of signal distributions, which includes the Gaussian, the quantizers with maximum output entropy (MOE) and minimum average error (MAE) are approximately the same within a multiplicative constant.