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This work compares two common approaches for classifying schizophrenia from EEG data—EEGNet, a compact convolutional neural network, and a Random Forest trained on spectral features—with an emphasis on how well they generalize across datasets. The models were trained on the ASZED-153 dataset using subject-level stratified cross-validation and then evaluated on a completely separate Kaggle EEG dataset collected under different recording conditions. While internal validation appeared reasonably encouraging (70.7% accuracy for EEGNet and 66.8% for Random Forest), performance dropped sharply on the external dataset (54.6% and 45.4%, respectively). This 16–21 percentage point decline was consistent with Maximum Mean Discrepancy results (MMD=0.0914), indicating meaningful distribution differences between datasets. A simple domain adaptation attempt (correlation alignment) provided only a modest improvement (about +1.2 percentage points) and did not recover internal performance levels. Overall, these findings highlight the practical challenge of developing EEG-based classifiers that remain reliable across recording sites and underscore the importance of external validation and more robust cross-site training strategies before considering any clinical deployment.