Entity matching (EM) is a critical step in entity resolution. Recently, entity matching based on large language models (LLMs) has shown great promise. However, current LLM-based entity matching approaches typically follow a binary matching paradigm that ignores the global consistency between different records. In this paper, we investigate various methodologies for LLM-based entity matching that incorporate record interactions from different perspectives. Specifically, we comprehensively compare three representative strategies: matching, comparing, and selecting, and analyze their respective advantages and challenges in diverse scenarios. Based on our findings, we further design a compositional entity matching (ComEM) framework that leverages the composition of multiple strategies and LLMs. In this way, ComEM can benefit from the advantages of different sides and achieve improvements in both effectiveness and efficiency. Experimental results show that ComEM not only achieves significant performance gains on various datasets but also reduces the cost of LLM-based entity matching in real-world application.