Conversational AI and Question-Answering systems (QASs) for knowledge graphs (KGs) are both emerging research areas: they empower users with natural language interfaces for extracting information easily and effectively. Conversational AI simulates conversations with humans; however, it is limited by the data captured in the training datasets. In contrast, QASs retrieve the most recent information from a KG by understanding and translating the natural language question into a formal query supported by the database engine. In this paper, we present a comprehensive study of the characteristics of the existing alternatives towards combining both worlds into novel KG chatbots. Our framework compares two representative conversational models, ChatGPT and Galactica, against KGQAN, the current state-of-the-art QAS. We conduct a thorough evaluation using four real KGs across various application domains to identify the current limitations of each category of systems. Based on our findings, we propose open research opportunities to empower QASs with chatbot capabilities for KGs. All benchmarks and all raw results are available1 for further analysis.