In many moderate dimensional applications we have multiple response variables that are associated with a common set of predictors. When the main objective is prediction of the response variables, a natural question is: do multivariate regression models that accommodate dependency among the response variables improve prediction compared to their univariate counterparts? Note that in this work, by univariate versus multivariate regression models, we refer to regression models with a single versus multiple response variables, respectively. We assume that both models have multiple covariates. Our question is motivated by an application in climate science, which involves the prediction of multiple metrics that measure the activity, intensity, severity etc. of a hurricane season. For moderate dimensional problems, our empirical results based on extensive simulation studies suggest that multivariate Bayesian methods can have a significant improvement in estimation; however, the gain in prediction is typically much less striking. We hope that our results will be useful for practitioners. This is joint work with Xun Li and Gabriele Villarini.