Supervised LLM finetuning involves training on input-output pairs, while unsupervised learning uses large amounts of unlabeled text data to improve general language understanding. Supervised learning offers precise control and task-specific performance but requires high-quality labeled datasets and can be limited in scope. Unsupervised learning is scalable and flexible but may require significant computational resources and can be harder to evaluate. When choosing between the two methods, consider factors such as data availability, task specificity, resources, control vs. flexibility, and ethical considerations.