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Parkinson’s disease (PD) is a progressive neurodegenerative disorder that impairs motor function, often causing tremors and difficulty with movement control. A promising diagnostic method involves analyzing hand-drawn patterns, such as spirals and waves, which show characteristic distortions in individuals with PD. This study compares three computational approaches for classifying individuals as Parkinsonian or healthy based on drawing-derived features: (1) Large Language Models (LLMs), (2) traditional machine learning (ML) algorithms, and (3) a fuzzy ontology-based method using fuzzy sets and Fuzzy-OWL2. Each method offers unique strengths: LLMs leverage pre-trained knowledge for subtle pattern detection, ML algorithms excel in feature extraction and predictive accuracy, and fuzzy ontologies provide interpretable, logic-based reasoning under uncertainty. Using three structured handwriting datasets of varying complexity, we assessed performance in terms of accuracy, interpretability, and generalization. Among the approaches, the fuzzy ontology-based method showed the strongest performance on complex tasks, achieving a high F1-score, while ML models demonstrated strong generalization and LLMs offered a reliable, interpretable baseline. These findings suggest that combining symbolic and statistical AI may improve drawing-based PD diagnosis.