Comparative latency analysis of cellular network control planes is an intuitive and effective method used to determine the superiority/inferiority of one cellular network over others. However, operational policies and network configurations vary across different networks, making it difficult to conduct fine-grained latency comparisons. We present a novel diagnostic method for the comparison of the latencies in processing control plane messages among cellular networks. For each cellular network, we automatically build a fine-grained state machine based on control plane signaling messages collected from user smartphones. From the state machines of multiple network operators, we identify common state transitions consisting of signaling messages. We then compare the latencies in the message intervals for each identified common transition. We discovered 38 bottleneck intervals from three representative control plane procedures by analyzing the state machines of five major operators. Our promising preliminary analysis deserves further research.