We present a comparison between two color equalization algorithms: Retinex, the famous model due to Land and McCann, and Automatic Color Equalization (ACE), a new algorithm recently presented by the authors. These two algorithms share a common approach to color equalization, but different computational models. We introduce the two models focusing on differences and common points. An analysis of their computational characteristics illustrates the way the Retinex approach has influenced ACE structure, and which aspects of the first algorithm have been modified in the second one and how. Their interesting equalization properties, like lightness and color constancy, image dynamic stretching, global and local filtering, and data driven dequantization, are qualitatively and quantitatively presented and compared, together with their ability to mimic the human visual system.