In-depth analysis of competitive debates is essential for participants to develop argumentative skills and refine strategies, and further improve their debating performance. However, manual analysis of unstructured and unlabeled textual records of debating is time-consuming and ineffective, as it is challenging to reconstruct contextual semantics and track logical connections from raw data. To address this, we propose Conch, an interactive visualization system that systematically analyzes both what is debated and how it is debated. In particular, we propose a novel parallel spiral visualization that compactly traces the multidimensional evolution of clash points and participant interactions throughout debate process. In addition, we leverage large language models with well-designed prompts to automatically identify critical debate elements such as clash points, disagreements, viewpoints, and strategies, enabling participants to understand the debate context comprehensively. Finally, through two case studies on real-world debates and a carefully-designed user study, we demonstrate Conch's effectiveness and usability for competitive debate analysis.