The continuous subgraph matching (CSM) problem aims to continuously detect patterns on a dynamic graph, with real-world applications such as fraud detection. Numerous methods have been proposed to address CSM, yet they lack fair comparisons. Furthermore, an existing unified framework for CSM shows misleading experimental results due to its suboptimal implementations. In this paper, we propose a new framework that generates CSM code from the logical and physical plans of delta queries with stacked views. By expressing each CSM method as a delta query plan, our framework enables fair comparisons of CSM methods. Through our comprehensive experiments, we make cause-and-effect arguments for the divergent performance trends from the previous papers and further analyze the individual impacts of various techniques on overall performance. Specifically, our CSM code for an old method significantly outperforms the most recent CSM method, CaLiG, by up to 48.6 times.