Background: In order to address the challenges in companies having no or limited effort datasets of their own, cross-company models have been a focus of interest for previous studies. Further, a particular domain of investigation has been Web projects. Aim: This study investigates to what extent effort predictions obtained using cross-company (CC) datasets are effective in relation to the predictions obtained using single-company (SC) datasets within the domain of web projects. Method: This study uses the Tukutuku database. We employed data on 125 projects from eight different companies and built cross and single-company models with stepwise linear regression (SWR) with and without relevancy filtering. We also benchmarked these models against mean and median based models. We report a case-by-case analysis per company as well as a meta-analysis of the findings. Results: Results showed that CC models provided poor predictions and performed significantly worse than SC models. However, relevancy filtered CC models yielded comparable results to that of SC models. These results corroborate with previous research. An interesting result was that the median-based models were consistently better than other models. Conclusions: We conclude that companies that carry out Web development may use a median-based CC model for prediction until it is possible for the company to build its own SC model, which can be used by itself or in combination with median-based estimations.