Argument structure prediction (ASP) constructs complete argument structures from discourse by identifying argumentative units and their relations. While recent work has explored diverse approaches---including unified neural models, multi-step pipelines, and prompt-based large language models (LLMs)---their relative trade-offs remain under-explored, particularly in dialogical settings. We present a systematic evaluation of ASP under strict schema constraints, comparing supervised fine-tuning and prompt-based LLMs across single- and multi-step task architectures, generating complete argument structures from dialogical input end-to-end. We benchmark them on three diverse dialogical corpora adapted from Inference Anchoring Theory into bipolar argument structures. Under a shared evaluation framework, we assess predictive performance, cross-domain generalization, schema compliance, and computational efficiency. Our results show that ASP remains a challenging task, with identifying argumentative relations emerging as the primary bottleneck, largely due to the implicit and context-dependent nature of dialogical argumentation. To facilitate future research, we release our data processing pipeline and end-to-end modeling framework for computational ASP on dialogical corpora.
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