Effective integration of renewables is essential in the energy transition, which necessitates efficient management of intermittent renewable energy generation, system cost minimization and continuous balance between supply and demand. Due to the problem's multifaceted nature, tools with a simplified representation of energy system operation are often used to ensure computational tractability, causing performance gaps between planning and operation stages. This work quantifies the gaps focusing on the impacts of model fidelity and dispatch strategy, such as the representation of physical constraints at different levels and varying forecast horizons. More specifically, a real-world case study with three energy hubs is considered. A Pareto front is first obtained considering the trade-offs between cost and carbon footprint using the Ehub tool, a state-of-the-art energy system planning tool. Following that, the cost-optimal and the emission-optimal designs are selected for evaluating the performance gaps, using the dispatch strategies obtained from the Ehub tool as the baseline. Results show that detailed considerations of physical constraints influence grid dependencies and fuel consumption but there are no significant impacts on resultant total costs. The cost increase due to detailed physical constraints is higher for the cost-optimal system than for the emission-optimal system. Moreover, limiting the forecast horizon to 24 hours has significant impacts on the emission-optimal system with an increase in total system cost by 20.3 %. In contrast, there is only a marginal increase of 0.8 % for the cost-optimal system.