While Large Language Models (LLMs) produce highly nuanced text simplifications, developers currently lack tools for a holistic, efficient, and reproducible diagnosis of their behavior. This paper introduces the Simplification Profiler, a diagnostic toolkit that generates a multidimensional, interpretable fingerprint of simplified texts. Multiple aggregated simplifications of a model result in a model's fingerprint. This novel evaluation paradigm is particularly vital for languages, where the data scarcity problem is magnified when creating flexible models for diverse target groups rather than a single, fixed simplification style. We propose that measuring a model's unique behavioral signature is more relevant in this context as an alternative to correlating metrics with human preferences. We operationalize this with a practical meta-evaluation of our fingerprints' descriptive power, which bypasses the need for large, human-rated datasets. This test measures if a simple linear classifier can reliably identify various model configurations by their created simplifications, confirming that our metrics are sensitive to a model's specific characteristics. The Profiler can distinguish high-level behavioral variations between prompting strategies and fine-grained changes from prompt engineering, including few-shot examples. Our complete feature set achieves classification F1-scores up to 71.9 %, improving upon simple baselines by over 48 percentage points. The Simplification Profiler thus offers developers a granular, actionable analysis to build more effective and truly adaptive text simplification systems.