Large language models (LLMs) differ in their moderation and content policies, which determine which prompts these models refuse to answer. These refusals can affect user decisions of which models to use and whether to make safe or risky prompts. Using data from LMArena, where users select preferred responses to their prompts from paired LLM comparisons, we estimate a discrete choice model that captures user preferences for making risky prompts and their choice of which model provides the best response quality given the possibility of refusals. We leverage this model to analyze how moderation policies affect market shares across proprietary and open-source LLMs. Our findings reveal that proprietary models provide higher quality responses and maintain larger market shares, but implement stricter moderation policies with higher refusal rates compared to open-source alternatives. This stricter moderation by proprietary models reduces market concentration by allowing lower-quality open-source models to compete effectively in the risky prompt segment. Mandating uniform moderation policies across all LLMs could increase market concentration favoring proprietary models, potentially hampering competition. Our framework provides a toolkit to evaluate the efficient frontier of moderation policies that minimize market concentration and increase safety.