Building datasets for dialogue tasks is expensive and time-consuming, requiring recruitment, training, and data collection from study participants. In response, much recent work has sought to use large language models (LLMs) to simulate both human-human and human-LLM interactions, as they have been shown to generate convincingly human-like text in many settings. However, how well do LLM-based simulations reflect real human dialogue? In this work, we answer this question by generating a large-scale dataset of 100,000 paired LLM-LLM and human-LLM dialogues from the WildChat dataset and quantifying how well the LLM simulations align with their human counterparts. Overall, we find relatively low alignment between simulations and human interactions, with systematic differences in multiple textual properties, including style and conversational dynamics. Further, we find that models perform similarly in simulating English, Chinese, and Russian dialogues. Our results also suggest that LLMs only simulate a narrow range of the overall distribution of human dialogue, as they perform better on the subset of humans who write similarly to the LLM’s own style.