Fine-tuning and prompting are two widely used approaches for adapting large language models to downstream tasks. However, their effectiveness on text simplification remains underexplored. We present SIMPLE, a comprehensive evaluation of large language model-based sentence simplification. We evaluate 12 open-weight large language models across diverse domains, including Wikipedia, medical, scientific, and news texts. In addition to standard evaluation metrics, we conduct a linguistic analysis of simplification outputs at the lexical, syntactic, and discourse levels. Our findings show that: 1) under practical deployment settings, QLoRA fine-tuning of base models performs better on Wikipedia-based simplification, whereas optimized prompting of instruction-tuned models performs better in non-Wikipedia domains; 2) QLoRA-fine-tuned models exhibit a strong alignment with human-written references across target readability levels, while prompted models show limited controllability over output difficulty; and 3) the primary discrepancies between large language model-generated simplifications and human references arise from syntactic restructuring and discourse coherence.