Children with Autism Spectrum Disorders (ASD) present significant difficulties to understand and express emotions. Systems have thus been proposed to provide objective measurements of acoustic features used by children suffering from ASD to encode emotion in speech. However, only a few studies have exploited such systems to compare different groups of children in their ability to express emotions, and even less have focused on the analysis of spontaneous emotion. In this contribution, we provide insights by extensive evaluations carried out on a new database of spontaneous speech inducing three emotion categories of valence (positive, neutral, and negative). We evaluate the potential of using an automatic recognition system to differentiate groups of children, i.e., pervasive developmental disorders, pervasive developmental disorders not-otherwise specified, specific language impairments, and typically developing, in their abilities to express spontaneous emotion in a common unconstrained task. Results show that all groups of children can be differentiated directly (diagnosis recognition) and indirectly (emotion recognition) by the proposed system.