Hypokinetic and hyperkinetic dysarthria are motor speech disorders that appear in patients with Parkinson's and Huntington's disease, respectively. They are caused due to progressive lesions or alterations in the basal ganglia. In particular, Huntington's disease (HD) is known to be more invasive and difficult to treat than Parkinson's disease (PD), producing more aggressive motor and cognitive alterations. Since speech production requires the movement and control of many different muscles and limbs, it constitutes a highly complex motor activity that may reflect relevant aspects of the patient's health state. This paper proposes the discrimination between patients with PD, HD, and healthy controls (HC) based on different speech dimensions. Speaker models based on Gaussian-mixture model supervectors are created with the features extracted from each speech dimension. The results suggest that it is possible to distinguish between PD and HD patients using the supervectors-based approach.