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Modern large language models (LLMs) employ diverse logical inference mechanisms for reasoning, making the strategic optimization of these approaches critical for advancing their capabilities. This paper systematically investigate the **comparative dynamics** of inductive (System 1) versus abductive/deductive (System 2) inference in LLMs. We utilize a controlled analogical reasoning environment, varying modality (textual, visual, symbolic), difficulty, and task format (MCQ / free-text). Our analysis reveals System 2 pipelines generally excel, particularly in visual/symbolic modalities and harder tasks, while System 1 is competitive for textual and easier problems. Crucially, task format significantly influences their relative advantage, with System 1 sometimes outperforming System 2 in free-text rule-execution. These core findings generalize to broader in-context learning. Furthermore, we demonstrate that advanced System 2 strategies like hypothesis selection and iterative refinement can substantially scale LLM reasoning. This study offers foundational insights and actionable guidelines for strategically deploying logical inference to enhance LLM reasoning.