This paper benchmarks multi-agent LLM architectures for residential home energy management using a full factorial experiment: four models spanning self-hosted to frontier (Llama 4 Maverick, DeepSeek-V3, GPT-4.1, and Claude Sonnet 4.6), three US utility tariff profiles, three household archetypes, and three random seeds across 108 seven-day simulations at hourly resolution. The central finding is that LLM-driven agents reliably achieve statistically equivalent cost reductions above 20% versus an unmanaged baseline, validating their practical viability for real-world deployment. Tariff complexity proves a stronger model differentiator than household size, with performance gaps widening significantly under real-time pricing structures. When savings performance is statistically equivalent across three models, the deployment decision reduces to cost: a 17x spread in API cost across models makes this a choice about efficiency, not capability.