Using Large Language Models (LLMs) for Information Extraction (IE) inherently involves transforming diverse textual inputs into strictly formatted outputs. Guaranteeing this structural validity introduces a hidden energy tax driven by constrained decoding mechanisms, serialisation formats, and underlying serving configurations. Consequently, standard token-level metrics fail to capture the true energy cost of generative IE, which also cannot be predicted by model size alone. To address this, we introduce the first dedicated benchmark evaluating the energy-accuracy trade-offs of generative IE. Our framework establishes task-aligned energy metrics, including Energy per True Positive (J/TP) and the F1-Energy Ratio (F₁/kJ). Through comprehensive ablation across architectures, decoding regimes, and serving-layer limits, we demonstrate that efficiency is governed by complex parameter interactions. We translate these findings into actionable configuration guidelines, equipping practitioners to maximise predictive accuracy, optimise energy yield, or achieve a sustainable Pareto balance.