Learned visual representations often capture large amounts of semantic information for accurate downstream applications. Human understanding of the world is fundamentally grounded in hierarchy. To mimic this and further improve representation capabilities, the community has explored "hierarchical'' visual representations that aim at modeling the underlying hierarchy of the visual world. In this work, we set out to investigate if hierarchical visual representations truly capture the human perceived hierarchy better than standard learned representations. To this end, we create HierNet, a suite of 12 datasets spanning 3 kinds of hierarchy from the BREEDs subset of ImageNet. After extensive evaluation of Hyperbolic and Matryoshka Representations across training setups, we conclude that they do not capture hierarchy any better than the standard representations but can assist in other aspects like search efficiency and interpretability. Our benchmark and the datasets are open-sourced at https://github.com/ethanlshen/HierNet.