A vast number of incoming bug reports demand effective methods to identify priority and severity for bug triaging. With increased technological advancement, machine learning and deep learning have been extensively examined to address this problem. Although Large Language Models (LLMs) such as Fine-tuned BERT (early generation LLM) have proven to capture context in the underlying textual data, severity and priority prediction demand additional features for understanding the relationships with other bug reports. This work utilizes the graph-based approach to model the bug reports and their other attributes, such as component, product and bug type information. It utilizes the relational intelligence of Graph Neural Network (GNN) to address the prioritization and severity assessment of bug reports in the Bugzilla bug tracking system. Initial tests on the Mozilla project dataset indicate that a project-wise predictive approach using GNNs yields higher accuracy in determining the priority and severity of bug reports compared to LLMs across multiple Mozilla projects, contributing to a notable advancement in the automation of bug severity and priority prediction tasks. Specifically, GNNs demonstrated a remarkable improvement over LLMs, increasing the priority prediction accuracy by $37%$ & $30%$ and severity prediction accuracy by $43%$ & $30%$ for Core and Firefox projects, respectively. Overall, GNN outperformed the Fine-tuned BERT (LLM) in predicting priority and severity for all the Mozilla projects.