This study compares the performance of two open-source large language models (LLMs)-Llama3-70B and DeepSeekR1-distill-Llama3-70B-on six biomedical text classification tasks. Four tasks involve data from social media, while two tasks focus on clinical notes from electronic health records, and all experiments were performed in zero-shot settings. Performance metrics, including precision, recall, and F1 scores, were measured for each task, along with their 95% confidence intervals. Results demonstrated that DeepSeekR1-distill-Llama3-70B generally performs better in terms of precision on most tasks, with mixed results on recall. While the zero-shot LLMs demonstrated high F1 scores for some tasks, they grossly underperformed on others, for data from both sources. The findings suggest that model selection should be guided by the specific requirements of the health-related text classification tasks, particularly when considering the precision-recall trade-offs, and that, in the presence of annotated data, supervised classification approaches may be more reliable than zero-shot LLMs.