In multi-gas climate policies such as the Kyoto Protocol one has to decide how to compare the emissions of different greenhouse gases. The choice of metric could have significant implications for mitigation priorities considered under the prospective negotiations for climate mitigation agreements. Several metrics have been proposed for this task with the Global Warming Potential (GWP) being the most common. However, these metrics have not been systematically compared to each other in the context of the 2 °C climate stabilization target. Based on a single unified modeling framework, we demonstrate that metric values span a wide range, depending on the metric structure and the treatment of the time dimension. Our finding confirms the basic salient point that metrics designed to represent different aspects of the climate and socio-economic system behave differently. Our result also reflects a complex interface between science and policy surrounding metrics. Thus, it is important to select or design a metric suitable for climate stabilization based on an interaction among practitioners, policymakers, and scientists.