Model Predictive Controls (MPCs) are a promising technique for managing building heating and cooling systems, balancing occupant needs with performance optimization. However, the practical large-scale deployment of MPCs is still hindered by the trade-off between computational effort and prediction accuracy, especially with complex thermal distribution systems. Previous work by the authors highlighted this challenge when a heating system is equipped with a stratified hot water tank as Thermal Energy Storage (TES). This paper examines the role of dynamic modeling of stratified TES in MPC prediction models. Two modeling techniques are compared: (i) a stratified tank with equal (fully mixed) volumes (“one-dimensional” model), and (ii) a tank with two movable stratification layers (“quasi-one-dimensional” model). These techniques are implemented in an MPC aiming to minimize the primary energy consumption of a heat pump heating system while maintaining user comfort. The MPCs are tested in a Hardware-in-the-Loop (HIL) setup, where the building is emulated and the heat pump, TES, and hydraulic circuits are real. The analysis aims to provide guidelines for MPC modeling and enhance the definition of MPC archetypes for heating systems in residential buildings.