•A systematic analysis of compatibility amongst building ontologies is undertaken.•Brick Schema, Project Haystack, RealEstateCore, and Digital Buildings are considered.•Diverse ontologies are evaluated by both the OQuaRE framework and an empirical study.•Ontology design patterns for smart building data interoperability are proposed. Ontologies play a critical role in data exchange, information integration, and knowledge sharing across diverse smart building applications. Yet, semantic differences between the prevailing building ontologies hamper their purpose of bringing data interoperability and restrict the ability to reuse building ontologies in real-world applications. In this paper, we propose and adopt a framework to conduct a systematic comparison and evaluation of four popular building ontologies (Brick Schema, RealEstateCore, Project Haystack, and Digital Buildings) from both axiomatic design and assertions in a use case, namely the Terminological Box (TBox) evaluation and the Assertion Box (ABox) evaluation. In the TBox evaluation, we use the SQuaRE-based Ontology Quality Evaluation (OQuaRE) framework and concede that Project Haystack and Brick Schema are more compact with respect to the ontology axiomatic design. In the ABox evaluation, we apply an empirical study with sample building data that suggests Brick Schema and RealEstateCore have greater completeness and expressiveness in capturing the main concepts and relations within the building domain. The results indicate that there is no universal building ontology for integrating Linked Building Data (LBD). We also discuss ontology compatibility and investigate building ontology design patterns (ODPs) to support ontology matching, alignment, and harmonisation.