Document AI (or Intelligent Document Processing) is a rapidly evolving field widely used to parse complex documents, yet its computational and environmental costs remain largely unquantified. To address this gap, this paper empirically evaluates the tradeoffs between accuracy and energy consumption across the three most representative categories of state-of-the-art open-source Document AI systems: pipeline tools, general-purpose Vision-Language Models (VLMs), and specialized VLMs. Using the reference benchmark OmniDocBench v1.5 and a controlled measurement protocol validated by physical wattmeters, we assess parsing performance alongside key sustainability metrics, including throughput, energy usage, and CO2eq emissions. Our findings reveal no strong correlation between parsing accuracy and energy consumption. Notably, specialized VLMs emerge as the most compelling category, with GLM-OCR achieving the best balance between accuracy and energy usage. In contrast, larger general-purpose models consume significantly more energy without necessarily delivering superior results. Moreover, pipeline tools demonstrate lower accuracy despite matching the energy footprint of specialized models. Finally, our extensive profiling shows that efficiency is heavily influenced by the hardware platform (CPU vs. GPU), the inference backend, and document characteristics, specifically length and complexity.