Overall persistence (POV) and long-range transport potential (LRTP) of chemicals are two indicators used in the context of precautionary chemical assessment. Multimedia fate models are used in research and regulatory contexts to calculate numerical indicators of POV and LRTP. The resulting indicator values exhibit uncertainty due to model uncertainty concerning model design and due to type A and B parameter uncertainty in the substance parameters. In this study, we compare the relative magnitude of parameter and model uncertainty for a large set of 3175 hypothetical chemicals that evenly cover the chemical parameter space and for eight different multimedia models available for the calculation of POV and LRTP. The assessment of the relative magnitude of the two types of uncertainty is important to direct further research and to inform the user on the level of confidence he can have in the model results. It is shown that, for POV, parameter uncertainty is larger than model uncertainty in most cases (78%), and that model uncertainty becomes more important for those chemicals which partition in considerable amounts into more than one environmental compartment. For LRTP, on the other hand, model uncertainty is higher than parameter uncertainty in most cases (75%). This dominance of model uncertainty can be explained with known differences in the model features. Uncertainty of POV can thus be reduced most effectively by improving data on degradation rate constants. For LRTP, the choice of the model that is best suited for the assessment purpose in question is most essential to reduce uncertainty.