Decarbonization efforts across North America, Europe, and beyond have prompted a rise in variable renewable energy sources, such as wind and solar, and investigations in alternative fuels to aid in the transition, such as hydrogen. These changes have prompted a need for more flexibility in the electric grid, as renewables are responsible for high variability in energy availability. Integrated energy systems (IESs) are well suited to provide this flexibility, but conventional technoeconomic modeling paradigms neglect the time-varying dynamic nature of the grid and thus undervalue resource flexibility. In this work, we develop a computational optimization framework for dynamic market-based technoeconomic comparison of IESs that co-produce low carbon electricity and hydrogen (e.g., solid oxide fuel cells, solid oxide electrolysis) against technologies that only produce electricity (e.g., natural gas combined cycle with carbon capture) or hydrogen. Our framework starts with rigorous physics-based process models, built in the IDAES-PSE open-source modeling platform, for six energy system concepts. Using data from these models, we train algebraic surrogate models, which enable tractable multi-period optimization of electricity and hydrogen coproduction based on energy prices. We repeat this analysis for all six concepts, 61 energy price scenarios, and five possible hydrogen selling prices and find solid oxide fuel cell-based coproduction systems achieve positive profits for 84%-86% of our tested market scenarios. From these market optimization results, we use multivariate linear regression to fit algebraic equations which predict optimized annual profit based on market features with R-squared values up to 0.99. The developed framework provides a powerful tool for direct comparison of flexible, multi-product energy system concepts to help discern optimal technology and integration options.