Automatic techniques in the context of motor speech disorders (MSDs) are typically two-class techniques aiming to discriminate between dysarthria and neurotypical speech or between dysarthria and apraxia of speech (AoS). Further, although such techniques are proposed to support the perceptual assessment of clinicians, the automatic and perceptual classification accuracy has never been compared. In this paper, we investigate a three-class automatic technique and a set of handcrafted features for the discrimination of dysarthria, AoS and neurotypical speech. Instead of following the commonly used One-versus-One or One-versus-Rest approaches for multi-class classification, a hierarchical approach is proposed. Further, a perceptual study is conducted where speech and language pathologists are asked to listen to recordings of dysarthria, AoS, and neurotypical speech and decide which class the recordings belong to. The proposed automatic technique is evaluated on the same recordings and the automatic and perceptual classification performance are compared. The presented results show that the hierarchical classification approach yields a higher classification accuracy than baseline One-versus-One and One-versus-Rest approaches. Further, the presented results show that the automatic approach yields a higher classification accuracy than the perceptual assessment of speech and language pathologists, demonstrating the potential advantages of integrating automatic tools in clinical practice.