Power-to-X (PtX) technologies are accelerating the energy transition. Increasingly, these technologies are also being leveraged as flexible energy resources to support the electrical grid. PtX models are often represented using a constant efficiency term as a linear relation between the power input and energy output. However, the operational performance of any PtX device such as an electrolyser or an electric heat pump can depend on factors such as operational temperature. In this paper, we have developed and analyzed two levels of model fidelity of the most widely assessed PtX technologies: electrolyser and heat pump systems. We assess the impact of detailed models on operation of PtX within simulation-based energy system analysis. Our results show that for electrolyser systems, the efficiency errors can be almost 0.6%. With heat pump systems, the difference in COP can be as high as 1.4.