Australia and the UK have developed contrasting approaches to the regulation of electronic cigarettes, with - broadly speaking - Australia adopting a relatively restrictive approach and the UK adopting a more permissive approach. Notably, these divergent policies were developed from the same broad evidence base. In this paper, to investigate differences in how the two jurisdictions manage and present evidence, we developed and evaluated a Large Language Model-based sentence classifier to perform automated analyses of electronic cigarette-related policy documents drawn from official Australian and UK legislative processes (109 documents in total). Specifically, we utilized GPT-4 to automatically classify sentences based on whether they contained claims that e-cigarettes were broadly helpful or harmful for public health. Our LLM-based classifier achieved an F-score of 0.9. Further, when applying the classifier to our entire sentence-level corpus, we found that Australian legislative documents show a much higher proportion of harmful statements, and a lower proportion of helpful statements compared to the expected values, with the opposite holding for the UK. In conclusion, this work utilized an LLM-based approach to provide evidence to support the contention that - drawing on the same evidence base - Australian ENDS-related policy documents emphasize the harms associated with ENDS products and UK policy documents emphasize the benefits. Further, our approach provides a starting point for using LLM-based methods to investigate the complex relationship between evidence and health policy formation.