Large language models (LLMs) have shown promise for automated patching, but their effectiveness depends strongly on how they are integrated into patching systems. While prior work explores prompting strategies and individual agent designs, the field lacks a systematic comparison of patching architectures. In this paper, we present a controlled evaluation of four LLM-based patching paradigms -- fixed workflow, single-agent system, multi-agent system, and general-purpose code agents -- using a unified benchmark and evaluation framework. We analyze patch correctness, failure modes, token usage, and execution time across real-world vulnerability tasks. Our results reveal clear architectural trade-offs: fixed workflows are efficient but brittle, single-agent systems balance flexibility and cost, and multi-agent designs improve generalization at the expense of substantially higher overhead and increased risk of reasoning drift on complex tasks. Surprisingly, general-purpose code agents achieve the strongest overall patching performance, benefiting from general-purpose tool interfaces that support effective adaptation across vulnerability types. Overall, we show that architectural design and iteration depth, rather than model capability alone, dominate the reliability and cost of LLM-based automated patching.