Ontology Matching (OM) is a critical task within the Semantic Web, addressing the challenge of semantic heterogeneity by identifying correspondences between entities from different ontologies. Traditional approaches often depend on predefined rules and external lexicons, while machine learning (ML) methods, including Deep Learning (DL) and Graph Neural Networks (GNNs), have gained traction due to their ability to generate expressive entity representations. However, existing GNN-based OM methods tend to focus predominantly on Graph Convolutional Networks (GCNs), overlooking the potential of other GNN architectures. To address this limitation, we introduce GNN-Match, a versatile framework that incorporates multiple GNN variants-Graph Transformer Networks (GTNs), Graph Attention Networks (GATs), Graph Isomorphism Networks (GINs), and GCNs. This framework allows users to select the most suitable GNN model to enhance semantic embeddings generated by a BERT-based encoder and capture structural features. Users can then aggregate these features using methods such as gated networks and concatenation, effectively capturing both semantic and structural information to optimize concept mapping. Extensive experiments across diverse datasets demonstrate that GNN variants consistently outperform non-GNN systems and offer new insights into the role of various GNN architectures in OM tasks.