Hierarchical document classification is essential for structuring large-scale textual corpora in domains such as digital libraries and academic repositories. While recent advances in large language models (LLMs) have opened new possibilities for text classification, their applicability to hierarchical settings under real-world constraints remains underexplored. This study investigates both generative and discriminative transformer-based models, evaluating their effectiveness across multiple inference strategies: zero-shot baseline, local fine-tuning, and a global approach using category-specific models. Experiments on two real-world hierarchical datasets provide a comprehensive comparison of classification accuracy, F1-macro scores, and inference times. The results highlight that, although generative LLMs can deliver competitive (yet variable) performance at higher levels of the hierarchy, their high inference costs hinder their use in time-sensitive applications. In contrast, fine-tuned discriminative models—particularly BERT-based architectures—consistently offer a more favorable trade-off between performance and efficiency.