Dysarthria due to Amyotrophic Lateral Sclerosis (ALS) and Parkinson’s Disease (PD) impairs sustained phoneme productions. Vowels and fricatives get affected differently owing to the differences in their production mechanisms. This paper examines three sustained voiceless fricatives - /s/, /sh/ and /f/, as compared to three sustained vowels - /a/, /i/ and /o/, for classifying patients with ALS/PD and Healthy Controls (HC). Fricatives are found to achieve higher classification accuracies than /a/ and /o/, though /i/ outperforms all. Patients seem to find it difficult to form constrictions while producing fricatives, or to proximally position the tongue and palate while uttering /i/, due to dysarthria. Unwanted voicing added to voiceless fricatives by the patient population further contributes towards the discrimination. Both source (related to vocal cord) and filter (related to vocal tract) cues of fricatives, on average, outperform those of vowels. Lastly, decision-level fusion of /i/-/s/-/sh/, with a pooled classifier for these three phonemes, achieves the highest mean ALS vs. HC classification accuracy of 83.35%, although in PD vs. HC case, fusion of multiple /i/ utterances performs the best with an accuracy of 80.03%.