Due to the crucial role conceptual models play in explicitly representing a subject domain, it is imperative that they are comprehensible and maintainable by humans. Modularization, i.e., decomposing an overarching, monolith model into smaller modules, is an established technique to make the model comprehensible and maintainable. Genetic Algorithms (GA) have been applied to modularize conceptual models by formulating desired structural model characteristics as multiple objectives. Recently, Graph Neural Networks (GNN)-based methods have shown promising performance in graph processing tasks, including graph clustering but outside the conceptual modeling domain. In this paper, we present a novel approach for GNN-based conceptual model modularization and comparatively analyze our approach against an existing multi-objective GA-based one. Furthermore, we provide a comparative analysis of our novel GNN model against two existing GNN-based graph clustering approaches. We investigate the dependence of the quality of the modularized solutions on the model size. We discuss the comparative results of our novel GNN-based approach and the existing GA-based approach to derive future research lines. Furthermore, our results show, that our proposed GNN-based modularization outperforms the existing GNN-based graph clustering approaches and provides a suitable alternative compared to the GA-based modularization.