Over the past decade, statisticians have developed methods to improve generalizations from nonrandom samples using propensity score methods. While these methods contribute to generalization research, their effectiveness is limited by small sample sizes. Small area estimation is a class of model-based methods that address the imprecision due to small samples and prior research has shown its potential to improve precision in generalization studies with small samples. However, the validity of both small area methods and existing design-based methods depend on the assumptions of propensity score models, leaving open the question of whether a specific method is preferred when core assumptions are violated. This study compares the performance of design-based and model-based estimators of population parameters in generalization studies when the assumptions for propensity score models are violated. Using a simulation study and an empirical example, we assess the sensitivity of the estimators under various degrees of violations in assumptions, discuss the advantages and tradeoffs of each approach, and highlight the implications for generalization research.