This paper compares the goods and characteristics models of the consumer within a traditional demand framework. We examine the nonparametric revealed preference conditions for the goods and characteristics models, and we develop a methodology for testing nested models of this class using nonparametric revealed preference techniques. Of primary interest is to make a comparison on the basis of predictive success, which requires that we develop a method to relate set predictions across models. This allows us to nonparametrically identify the model which best fits the data, and in doing so, to identify the value added by the characteristics structure in explaining consumer behavior. We then explore the effects of hypothetical price variation as implied by our findings in order to nonparametrically bound any comparative statics of interest. We implement these procedures on household panel data from the UK milk market. The primary result is that the better fit of the characteristics model is entirely attributable to dimension reduction.