In this work, we focus on distributed cache systems with non-uniform storage capacity across caches. We compare the performance of our system with the performance of a system with the same cumulative storage distributed evenly across the caches. We characterize the extent to which the performance of the distributed cache system deteriorates due to storage heterogeneity. The key takeaway from this work is that the effects of heterogeneity in the storage capabilities depend heavily on the popularity profile of the contents being cached and delivered. We analytically show that compared to the case where contents popularity is comparable across contents, lopsided popularity profiles are more tolerant to heterogeneity in storage capabilities. We validate our theoretical results via simulations.