A considerable amount of attention has been paid lately to a number of data hiding methods based in quantization, seeking to achieve in practice the results predicted by Costa (1983) for a channel with side information at the encoder. With the objective of filling a gap in the literature, this paper supplies a fair comparison between significant representatives of both this family of methods and the former spread-spectrum approaches that make use of near-optimal ML decoding; the comparison is based on measuring their probabilities of decoding error in the presence of channel distortions. Accurate analytical expressions and tight bounds for the probability of decoding error are given and validated by means of Monte Carlo simulations. For dithered modulation (DM), a novel technique that allows us to obtain tighter bounds to the probability of error is presented. Within the new framework, the strong points and weaknesses of both methods are distinctly displayed. This comparative study allows us to propose a new technique named "quantized projection" (QP), which, by adequately combining elements of those previous approaches, produces gains in performance.