This study evaluates the ability of DeepSeek, an open-source large language model (LLM), to simulate public opinions in comparison to LLMs developed by major tech companies. By comparing DeepSeek-R1 and DeepSeek-V3 with Qwen2.5, GPT-4o, and Llama-3.3 and utilizing survey data from the American National Election Studies (ANES) and the Zuobiao dataset of China, we assess these models' capacity to predict public opinions on social issues in both China and the United States, highlighting their comparative capabilities between countries. Our findings indicate that DeepSeek-V3 performs best in simulating U.S. opinions on the abortion issue compared to other topics such as climate change, gun control, immigration, and services for same-sex couples, primarily because it more accurately simulates responses when provided with Democratic or liberal personas. For Chinese samples, DeepSeek-V3 performs best in simulating opinions on foreign aid and individualism but shows limitations in modeling views on capitalism, particularly failing to capture the stances of low-income and non-college-educated individuals. It does not exhibit significant differences from other models in simulating opinions on traditionalism and the free market. Further analysis reveals that all LLMs exhibit the tendency to overgeneralize a single perspective within demographic groups, often defaulting to consistent responses within groups. These findings highlight the need to mitigate cultural and demographic biases in LLM-driven public opinion modeling, calling for approaches such as more inclusive training methodologies.