The Rotterdam model and the Almost Ideal Demand System (AIDS) are often applied in consumer demand systems modeling. Using Monte Carlo techniques, we determine which model performs best in recovering the true elasticities of demand. The AIDS model is usually used in linearized form. Since the Rotterdam model is also linear in a very similar form, comparison of the Rotterdam model and the AIDS model has been the subject of much speculation in the literature. We not only compare the linearized AIDS model with the Rotterdam model, but also with the full nonlinear AIDS.