Automatic music genre classification is a long-standing challenge in Music Information Retrieval (MIR); work on non-Western music traditions remains scarce. Nepali music encompasses culturally rich and acoustically diverse genres--from the call-and-response duets of Lok Dohori to the rhythmic poetry of Deuda and the distinctive melodies of Tamang Selo--that have not been addressed by existing classification systems. In this paper, we construct a novel dataset of approximately 8,000 labeled 30-second audio clips spanning eight Nepali music genres and conduct a systematic comparison of nine classification models across two paradigms. Five classical machine learning classifiers (Logistic Regression, SVM, KNN, Random Forest, and XGBoost) are trained on 51 hand-crafted audio features extracted via Librosa, while four deep learning architectures (CNN, RNN, parallel CNN-RNN, and sequential CNN followed by RNN) operate on Mel spectrograms of dimension 640 x 128. Our experiments reveal that the sequential Convolutional Recurrent Neural Network (CRNN)--in which convolutional layers feed into an LSTM--achieves the highest accuracy of 84%, substantially outperforming both the best classical models (Logistic Regression and XGBoost, both at 71%) and all other deep architectures. We provide per-class precision, recall, F1-score, confusion matrices, and ROC analysis for every model, and offer a culturally grounded interpretation of misclassification patterns that reflects genuine overlaps in Nepal's musical traditions.