The authors study a one-dimensional abstract model for classical and quantum irregular scattering in which the interacting dynamics is defined by the standard map. This model allows for a direct comparison of classical and quantum transport properties. Whereas the classical model is characterized by chaotic diffusion, in the quantum case the interplay of diffusion and localization determines a transition from a ballistic regime to a localized one, with an intermediate ohmic regime in the crossover region. The scattering matrix is numerically computed by solving a Lippman-Schwinger equation. In the ballistic regime the S-matrix fluctuations are found to share some typical features with the Ericson fluctuations, with correlation lengths close to the classical rates of exponential decay. Qualitative modifications occurring in the diffusive regime, including universal transmission fluctuations, are discussed.