This article presents a comparative analysis of the ability of two large language model (LLM)-based chatbots, ChatGPT and Bing Chat, recently rebranded to Microsoft Copilot, to detect veracity of political information. We use AI auditing methodology to investigate how chatbots evaluate true, false, and borderline statements on five topics: COVID-19, Russian aggression against Ukraine, the Holocaust, climate change, and LGBTQ+ related debates. We compare how the chatbots perform in high- and low-resource languages by using prompts in English, Russian, and Ukrainian. Furthermore, we explore the ability of chatbots to evaluate statements according to political communication concepts of disinformation, misinformation, and conspiracy theory, using definition-oriented prompts. We also systematically test how such evaluations are influenced by source bias which we model by attributing specific claims to various political and social actors. The results show high performance of ChatGPT for the baseline veracity evaluation task, with 72 percent of the cases evaluated correctly on average across languages without pre-training. Bing Chat performed worse with a 67 percent accuracy. We observe significant disparities in how chatbots evaluate prompts in high- and low-resource languages and how they adapt their evaluations to political communication concepts with ChatGPT providing more nuanced outputs than Bing Chat. Finally, we find that for some veracity detection-related tasks, the performance of chatbots varied depending on the topic of the statement or the source to which it is attributed. These findings highlight the potential of LLM-based chatbots in tackling different forms of false information in online environments, but also points to the substantial variation in terms of how such potential is realized due to specific factors, such as language of the prompt or the topic.