Using speech samples as a biomarker is a promising avenue for detecting and monitoring the progression of Parkinson's disease (PD), but there is considerable disagreement in the literature about how best to collect and analyze such data. Early research in detecting PD from speech used a sustained vowel phonation (SVP) task, while some recent research has explored recordings of more cognitively demanding tasks. To assess the role of language in PD detection, we tested pretrained models with varying data types and pretraining objectives and found that (1) text-only models match the performance of vocal-feature models, (2) multilingual Whisper outperforms self-supervised models whereas monolingual Whisper does worse, and (3) AudioSet pretraining improves performance on SVP but not spontaneous speech. These findings together highlight the critical role of language for the early detection of Parkinson's disease.