Estimating cognitive or affective states from brain signals is a key but challenging step in creating passive brain-computer interface (BCI) applications. So far, estimating mental workloads or emotions from electroencephalogram (EEG) signals is only feasible with modest classification accuracies, which thus lead to unreliable neuroadaptive applications. However, recent machine-learning algorithms, notably Riemannian geometry-based classifiers (RGCs) and convolutional neural networks (CNNs), have shown promise for other BCI systems, e.g., motor imagery BCIs. However, they have not been formally studied and compared for cognitive or affective states classification.