In energy system models, computational tractability is often maintained by adopting a simplified temporal and spatial representation in a deterministic model formulation i.e., neglecting uncertainty. However, such simplifications have been shown to impact the optimal result. To address the question of how to prioritize the limited computational resources, the trade-off between spatial resolution and uncertainty is assessed by applying a novel method based on global sensitivity analysis to a peer-reviewed heat decarbonization model. For all output variables apart from the total system and fuel cost, spatial resolution is ranks amongst the five most important model inputs. It is the most relevant factor for investment decisions on network capacities. For the total fuel consumption and emissions, spatial resolution turns out to be more relevant than the fuel prices themselves. Compared across all outputs, the analysis suggests the impact of spatial resolution is comparable the impact of heat demand levels and the discount rate.