While the large energy consumption of Large Language Models (LLMs) is recognized by the community, system operators lack guidance for energy-efficient LLM inference deployments that leverage energy trade-offs of heterogeneous hardware due to a lack of energy-aware benchmarks and data. In this work we address this gap with Watt Counts: the largest open-access dataset of energy consumption of LLMs, with over 5,000 experiments for 50 LLMs across 10 NVIDIA Graphics Processing Units (GPUs) in batch and server scenarios along with a reproducible, open-source benchmark that enables community submissions to expand this dataset. Leveraging this dataset, we conduct a system-level study of LLM inference across heterogeneous GPU architectures and show that GPU selection is crucial for energy efficiency outcomes and that optimal hardware choices vary significantly across models and deployment scenarios, demonstrating the critical importance of hardware-aware deployment in heterogeneous LLM systems. Guided by our data and insights, we show that practitioners can reduce energy consumption by up to 70% in server scenarios with negligible impact on user experience, and by up to 20% in batch scenarios.