If disentangled properly, patterns distilled from evolutionarily related sequences of a given protein family can inform their traits - such as their structure and function. Recent years have seen an increase in the complexity of generative models towards capturing these patterns; from sitewise to pairwise to deep and variational. In this study we evaluate the degree of structure and fitness patterns learned by a suite of progressively complex models. We introduce pairwise saliency, a novel method for evaluating the degree of captured structural information. We also quantify the fitness information learned by these models by using them to predict the fitness of mutant sequences and then correlate these predictions against their measured fitness values. We observe that models that inform structure do not necessarily inform fitness and vice versa, contrasting recent claims in this field. Our work highlights a dearth of consistency across fitness assays as well as divergently provides a general approach for understanding the pairwise decomposable relations learned by a given generative sequence model.