Lung cancer is the leading cause of cancer mortality worldwide, and non-invasive methods for detecting key mutations and staging are essential for improving patient outcomes. Here, we compare the performance of two machine learning models - FMCIB+XGBoost, a supervised model with domain-specific pretraining, and Dinov2+ABMIL, a self-supervised model with attention-based multiple-instance learning - on 3D lung nodule data from the Stanford Radiogenomics and Lung-CT-PT-Dx cohorts. In the task of KRAS and EGFR mutation detection, FMCIB+XGBoost consistently outperformed Dinov2+ABMIL, achieving accuracies of 0.846 and 0.883 for KRAS and EGFR mutations, respectively. In cancer staging, Dinov2+ABMIL demonstrated competitive generalization, achieving an accuracy of 0.797 for T-stage prediction in the Lung-CT-PT-Dx cohort, suggesting SSL's adaptability across diverse datasets. Our results emphasize the clinical utility of supervised models in mutation detection and highlight the potential of SSL to improve staging generalization, while identifying areas for enhancement in mutation sensitivity.