A Digital Twin (DT) is a purposeful digital representation of a physical entity that employs data, algorithms, and software to enhance operations, making it possible to e.g., forecast failures, or evaluate new designs through the simulation of real-world scenarios. DTs are enablers for real-time monitoring, simulation, and optimization. However, traditional simulation DTs often rely on complex, non-linear mechanistic models with high computational demands, complex structures, and a large number of specific parameters and thus pose quite a challenge to maintainability. Surrogate models, on the other hand, are simplified approximations of more complex, higher-order models. These approximations are typically built using data-driven approaches, such as Random Forest Regression, facilitating faster simulations, simpler adaptation, and quicker deployment. This study analyzes the complexity of mechanistic and surrogate modeling approaches in the context of DTs to aid model selection. A model with reduced complexity enhances computational efficiency, simplifies implementation, and supports real-time monitoring and predictive maintenance. Complexity analysis evaluates metrics such as analytical, structural, space, behavioral, training, and prediction complexity, resulting in an overall complexity score for model selection. However, the decision involves trade-offs, such as balancing high fidelity with low complexity or prioritizing high explainability over structural simplicity. Addressing these trade-offs is essential in selecting a model that balances the accuracy, usability, and efficiency of DTs. Using a stirred tank reactor as a use case, the mechanistic model is compared to a surrogate model to quantify complexity scores and select a less complex model for DT development.