In order to learn better about how different visual recognition backbones make decisions, we propose a methodology that systematically applies deep explanation algorithms on a dataset-wide basis, and compares the statistics generated from the amount and nature of the explanations to gain insights about the decision-making of different models. Specifically, we propose two methodologies called sub-explanation counting and cross-testing. These methodologies reveal the difference among networks in terms of two properties called compositionality and disjunctivism. Transformers and ConvNeXt are found to be more compositional, in the sense that they jointly consider multiple parts of the image in building their decisions, whereas traditional CNNs and distilled transformers are less compositional and more disjunctive, which means that they use multiple diverse but smaller set of parts to achieve a confident prediction. Through further experiments, we pinpointed the choice of normalization to be especially important in the compositionality of a model, in that batch normalization leads to less compositionality while group and layer normalization lead to more. Finally, we also analyze the features shared by different backbones and plot a landscape of different models based on their feature-use similarity.