This paper presents a physically consistent channel model for stacked intelligent metasurfaces (SIM) aided communication systems, considering both diagonal RIS (D-RIS) and beyond diagonal RIS (BD-RIS) implementations. The model accounts for mutual coupling effects and clarifies the assumptions needed to derive a simplified model used in previous works. The study shows that a 1-layer SIM implemented with BD-RIS achieves the performance upper bound with limited complexity, while any L-layer SIM implemented with D-RIS is suboptimal. The model is derived using multiport network theory, which allows for the cascading of multiple blocks, each consisting of a wireless channel and an RIS. The scattering matrix of the entire channel is derived by cascading the scattering matrices of individual blocks and the receiver channel. The simplified model assumes unilateral behavior and no mutual coupling, leading to a more straightforward expression for the channel matrix. The study also compares the performance of SIMs implemented with D-RIS and BD-RIS, showing that BD-RIS provides better performance, especially for a single-layer configuration. Numerical results confirm that 1-layer SIMs with BD-RIS achieve the upper bound of performance and have lower circuit complexity compared to D-RIS implementations. The paper concludes that SIM-aided systems can benefit from BD-RIS due to their enhanced flexibility and performance.This paper presents a physically consistent channel model for stacked intelligent metasurfaces (SIM) aided communication systems, considering both diagonal RIS (D-RIS) and beyond diagonal RIS (BD-RIS) implementations. The model accounts for mutual coupling effects and clarifies the assumptions needed to derive a simplified model used in previous works. The study shows that a 1-layer SIM implemented with BD-RIS achieves the performance upper bound with limited complexity, while any L-layer SIM implemented with D-RIS is suboptimal. The model is derived using multiport network theory, which allows for the cascading of multiple blocks, each consisting of a wireless channel and an RIS. The scattering matrix of the entire channel is derived by cascading the scattering matrices of individual blocks and the receiver channel. The simplified model assumes unilateral behavior and no mutual coupling, leading to a more straightforward expression for the channel matrix. The study also compares the performance of SIMs implemented with D-RIS and BD-RIS, showing that BD-RIS provides better performance, especially for a single-layer configuration. Numerical results confirm that 1-layer SIMs with BD-RIS achieve the upper bound of performance and have lower circuit complexity compared to D-RIS implementations. The paper concludes that SIM-aided systems can benefit from BD-RIS due to their enhanced flexibility and performance.