Deep learning (DL) methods are increasingly outperforming classical approaches in brain imaging, yet their generalizability across diverse imaging cohorts remains inadequately assessed. As age and sex are key neurobiological markers in clinical neuroscience, influencing brain structure and disease risk, this study evaluates three of the existing three-dimensional architectures, namely Simple Fully Connected Network (SFCN), DenseNet, and Shifted Window (Swin) Transformers, for age and sex prediction using T1-weighted MRI from four independent cohorts: UK Biobank (UKB, n=47,390), Dallas Lifespan Brain Study (DLBS, n=132), Parkinson's Progression Markers Initiative (PPMI, n=108 healthy controls), and Information eXtraction from Images (IXI, n=319). We found that SFCN consistently outperformed more complex architectures with AUC of 1.00 [1.00-1.00] in UKB (internal test set) and 0.85-0.91 in external test sets for sex classification. For the age prediction task, SFCN demonstrated a mean absolute error (MAE) of 2.66 (r=0.89) in UKB and 4.98-5.81 (r=0.55-0.70) across external datasets. Pairwise DeLong and Wilcoxon signed-rank tests with Bonferroni corrections confirmed SFCN's superiority over Swin Transformer across most cohorts (p<0.017, for three comparisons). Explainability analysis further demonstrates the regional consistency of model attention across cohorts and specific to each task. Our findings reveal that simpler convolutional networks outperform the denser and more complex attention-based DL architectures in brain image analysis by demonstrating better generalizability across different datasets.