Meta-analytical-predictive (MAP) prior has been widely used in borrowing summary-level historical control data. One highly desired feature for the MAP prior is the ability to dynamically down-weight the historical data in the presence of a prior-data conflict. The robust MAP (rMAP) prior was proposed to strengthen this feature by adding a non-informative component to the original MAP prior. An alternative robustification approach utilizes the same underlying idea as the rMAP and has a Bayesian model averaging interpretation. In this research, we explore the connection and differences between the two methods, and compare their performances using simulation studies.