Nonparametric Bayesian models are becoming increasingly popular as they allow us to fit more robust models than their parametric counterparts. In recent Bayesian applications, Dirichlet Process (DP) based models are commonly used to fit Bayesian models under flexible distributional assumptions. In this article we compare parametric and Dirichlet process based hierarchical Bayesian models and show that while hierarchical DP models may provide flexibility in model fit, they may not perform uniformly better in other aspects as compared to the parametric models.