Digital image compression reduces the bandwidth, time, and energy needed for transmission of images and signals, as well as memory needed for their storage. However, it cannot solve the digitization problems. Recently proposed compressive sampling (or sensing) solves these problems by reducing the average number of projections required for representing images and signals through exploiting their sparsity. An alternative approach named compressive quantization solves identical problems by reducing the average number of bits required for the same purpose. It exploits statistical properties of images and signals, as well as specific features of quantizers. In this paper, the analysis and further development of compressive quantization used for digitization of images is combined with its comparison to compressive sampling. It is shown that compressive quantization simplifies the image digitization more significantly and provides more effective and less distorting compression than compressive sampling. Its practical realization is much easier than that of compressive sampling. The root causes of these advantages are revealed.