The design and operation of integrated multi-energy systems require models that adequately describe the behavior of conversion and storage technologies. Typically, linear conversion performance or fixed data from technology manufacturers are employed, especially for new or advanced technologies. This contribution provides a new modeling framework for electrochemical devices, that bridges first-principles models to their simplified implementation in the optimization routine. First, thermodynamic models are implemented to determine the on/off-design performance and dynamic behavior of different types of fuel cells and of electrolyzers. Then, as such nonlinear models are intractable for use in the optimization of integrated systems, different linear approximations are developed. The proposed strategies for the synthesis of reduced order models are compared to assess the impact of modeling approximations on the optimal design of multi-energy systems including fuel cells and electrolyzers. This allows to determine the most suitable level of detail for modeling the underlying electrochemical technologies from an integrated system perspective. It is found that the approximation methodology affects both the design and operation of the system, with a significant effect on system costs and violation of the thermal energy demand. Finally, the optimization and technology modeling framework is exploited to determine guidelines for the installation of the most suitable fuel cell technology in decentralized multi-energy systems. We show how the installation costs of PEMFC, SOFC and MCFC, their electrical and thermal efficiencies, their conversion dynamics, and the electricity price affect the system design and technology selection.