Large Language Models (LLMs) are increasingly used in clinical applications. However, their behavior remains highly sensitive to subtle linguistic variations, such as rephrasing or syntactic variation. This sensitivity poses risks in safety-critical healthcare settings, where semantically equivalent inputs should produce consistent predictions. However, a key challenge is to ensure that prompt variations truly preserve clinical meaning, as embedding-based similarity metrics often fail to capture distinctions involving negation, temporality, or severity. To address this limitation, we propose a semantic verification framework based on Natural Language Inference (NLI) to filter meaning-preserving prompt variations, which are further refined using an LLM-as-a-judge and audited by a clinical expert. In addition, we introduce three metrics to quantify model sensitivity: MeaningPreserving Variation Sensitivity (MVS), confidence variation (ΔC), and Worst-Case Instability (WCI). We evaluate 16 open-source general-purpose (GP) and medical LLMs within the same model families and parameter scales, using reformulated prompts derived from the DiagnosisQA and MedQA datasets. Our results demonstrate that robustness differences between domain-specific (DS) models are mixed and highly model-dependent, i.e., domain specialization does not consistently improve or reduce robustness to meaning-preserving prompt reformulations. Several DS models rank among the most robust (when compared with GP counterparts), and strong GP baselines remain competitive as well.