The intermittency of wind and solar power leads to periods of excess generation, necessitating storage options, such as converting it into hydrogen. In microgrids, alternatively, the surplus renewable electricity can be used to generate heat via heat pumps to satisfy local heating demand. This study compares these two pathways by modeling a large-scale IEEE 84-bus system under a day-ahead scheduling framework that incorporates an electrolyzer–storage–fuel cell hydrogen chain and ground-source heat pumps (GSHPs). Thermal energy storage enables time-shifting of thermal supply. A multi-objective optimization framework maximizes operating profit, minimizes emissions, and reduces voltage deviation, incorporating uncertainties in wind, solar, and market prices. Results show hydrogen storage operates below 27% round-trip efficiency, whereas GSHPs achieve a COP over 5, making them operationally more cost-effective for allocating surplus electricity within the day-ahead scheduling horizon. Using GSHPs also shows substantial short-term operating cost and emission advantages compared to burning natural gas in boilers. However, GSHP operation is significantly curtailed in the voltage-minimizing solution due to increased network current flows.