Resting-state functional connectivity is widely used in machine learning-based classification of neuropsychiatric disorders. Quantum machine learning models have been proposed for functional connectivity data, but few studies have evaluated them under leave-site-out validation or against matched classical models. We compared six quantum model families with classical ones using identical correlation-derived features across four public cohorts (4,308 subjects). Leave-site-out validation was used for the Autism Brain Imaging Data Exchange (ABIDE I), ADHD-200 (attention-deficit/hyperactivity disorder), and REST-meta-MDD (major depressive disorder) cohorts, while the UCLA Consortium for Neuropsychiatric Phenomics (UCLA-CNP) was evaluated using stratified 10-fold cross-validation. The quantum kernel was statistically indistinguishable from a matched classical kernel across all four cohorts, with the average accuracy difference within 1.4 percentage points at 95% confidence. On ABIDE I, a hybrid quantum convolutional network achieved similar accuracy to its classical counterpart (0.645 vs. 0.641), while a trainable quantum kernel exceeded its classical counterpart by 0.064 in area under the curve (AUC). Quantum convolutional networks also achieved higher AUC than their matched classical networks on this cohort and showed smaller train-test gaps on all four cohorts, without an accuracy gain. Overall, most quantum models matched their classical counterparts, but none consistently outperformed them. This study, among the first quantum evaluations of ABIDE I under leave-site-out validation, provides a feature-matched benchmark of quantum and classical models comprising 284 matched comparisons. We further analyse fidelity-based graph construction and account for the observed quantum-classical parity through effective-dimension and eigenspectrum analyses.

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