Although it is widely acknowledged that adding class disjointness to ontologies enables a wide range of interesting applications, this type of axiom is rarely used on today’s Semantic Web. This is due to the enormous skill and effort required to make the necessary modeling decisions. Automatically generating disjointness axioms could lower the barrier of entry and lead to a wider spread adoption. Different methods have been proposed for this automatic generation. These include supervised, top-down approaches which base their results on heterogeneous types of evidence and unsupervised, bottom-up approaches which rely solely on the instance data available for the ontology. However, current literature is missing a thorough comparison of these approaches. In this article, we provide this comparison by presenting two fundamentally different state-of-the-art approaches and evaluating their relative ability to enrich a well-known, multi-purpose ontology with class disjointness. To do so, we introduce a high-quality gold standard for class disjointness. We describe the creation of this standard in detail and provide a thorough analysis. Finally, we also present improvements to both approaches, based in part on discoveries made during our analysis and evaluation.