Automated dementia screening enables early detection and intervention, reducing costs to healthcare systems and increasing quality of life for those affected. Depression has shared symptoms with dementia, adding complexity to diagnoses. The research focus so far has been on binary classification of dementia (DEM) and healthy controls (HC) using speech from picture description tests from a single dataset. In this work, we apply established baseline systems to discriminate cognitive impairment in speech from the semantic Verbal Fluency Test and the Boston Naming Test using text, audio and emotion embeddings in a 3-class classification problem (HC vs. MCI vs. DEM). We perform cross-corpus and mixed-corpus experiments on two independently recorded German datasets to investigate generalization to larger populations and different recording conditions. In a detailed error analysis, we look at depression as a secondary diagnosis to understand what our classifiers actually learn.