With the growth of ocean transport and with increasing vessel sizes, managing congestion at the landside of container terminals has become a major challenge. The landside of a sea terminal handles containers that arrive or depart via train or truck. Large sea terminals have to handle thousands of trucks and dozens of trains per day. As trains run on fixed schedule, their containers are prioritized in stacking and internal transport handling. This has consequences for the service of external trucks, which might be subject to delays. We analyze the impact of prioritization on such delays using a stochastic stylized semi-open queuing network model with bulk arrivals (of containers on trains), shared stack crane resources, and multi-class containers. We use the theory of regenerative processes and Markov chain analysis to analyze the network. The proposed network solution algorithm works for large-scale systems and yields sufficiently accurate estimates for performance measurement. The model can capture priority service for containers at the shared stack cranes, while preserving strict handling priorities. The model is used to explore the choice of different internal transport vehicles (with coupled versus decoupled operations at the stack and train gantry cranes) to understand the effect on delays. Our results show that decoupled transport vehicles in comparison to coupled vehicles can mitigate the external truck container handling delays at shared stack cranes by a large extent (up to 12%). However, decoupled vehicles marginally increase the train container handling delays at shared stack cranes (up to 6%). When train arrival rates are low, prioritizing the handling of train containers at the stack cranes significantly reduces their delays. Further, such prioritization hardly delays external truck containers.