The speech of people with Parkinson's Disease (PD) has been shown to hold important clues about the presence and progression of the disease. We investigate the factors based on which humans experts make judgments of the presence of disease in speech samples over five different speech tasks: phonations, sentence repetition, reading, recall, and picture description. We make comparisons by conducting listening tests to determine clinicians accuracy at recognizing signs of PD from audio alone, and we conduct experiments with a machine learning system for detection based on Whisper. Across tasks, Whisper performs on par or better than human experts when only audio is available, especially on challenging but important subgroups of the data: younger patients, mild cases, and female patients. Whisper's ability to recognize acoustic cues in difficult cases complements the multimodal and contextual strengths of human experts.