It is now widely accepted that there is a functional relationship between the speech perception and production systems in the human brain. However, the precise mechanisms and role of this relationship still remain debated. The question of invariance and robustness in categorization are set at the center of the debate: how is stable information extracted from the variable sensory input in order to achieve speech comprehension? In this context, auditory (resp. motor, perceptuo-motor) theories propose that speech is categorized thanks to auditory (resp. motor, perceptuo-motor) processes. However, experimental evidence is still scarce and does not allow to clearly distinguish between the current theories and determine whether invariance in speech perception is of an auditory or motor type. This is why we developed COSMO, a Bayesian model comparing sensory and motor processes in the form of probability distributions which enable both theoretical developments and quantitative simulations. A first significant result in COSMO is an indistinguishability theorem: it is only by simulations of adverse conditions or partial learning that the specificity of sensory vs. motor processing can emerge and provide a basis for evaluation of the specific role of each sub-system. We present the COSMO model, and how its sensory and motor sub-systems are learned, then we describe simulations exploring the way these sub-systems differ during speech categorization. We discuss the experimental results in the light of a “narrowband vs. wideband” interpretation: the sensory sub-system is more precisely tuned to the frequently learned sensory input and hence more efficient in recognizing these inputs, providing a “narrowband” system. Conversely, the motor sub-system is less accurate to recognize learned sensory inputs but it has better generalization properties, making it more robust to unexpected variability which would provide it with “wideband” characteristics.