The rapid proliferation of recent Multi-Agent Systems (MAS), where Large Language Models (LLMs) and Large Reasoning Models (LRMs) usually collaborate to solve complex problems, necessitates a deep understanding of the persuasion dynamics that govern their interactions. This paper challenges the prevailing hypothesis that persuasive efficacy is primarily a function of model scale. We propose instead that these dynamics are fundamentally dictated by a model's underlying cognitive process, especially its capacity for explicit reasoning. Through a series of multi-agent persuasion experiments, we uncover a fundamental trade-off we term the Persuasion Duality. Our findings reveal that the reasoning process in LRMs exhibits significantly greater resistance to persuasion, maintaining their initial beliefs more robustly. Conversely, making this reasoning process transparent by sharing the "thinking content" dramatically increases their ability to persuade others. We further consider more complex transmission persuasion situations and reveal complex dynamics of influence propagation and decay within multi-hop persuasion between multiple agent networks. This research provides systematic evidence linking a model's internal processing architecture to its external persuasive behavior, offering a novel explanation for the susceptibility of advanced models and highlighting critical implications for the safety, robustness, and design of future MAS.