The widespread adoption of IoT has driven the development of cyber-physical systems (CPS) in industrial environments, leveraging Industrial IoTs (IIoTs) to automate manufacturing processes and enhance productivity. The transition to autonomous systems introduces significant operational costs, particularly in terms of energy consumption. Accurate modeling and prediction of IIoT energy requirements are critical, but traditional physics- and engineering-based approaches often fall short in addressing these challenges comprehensively. In this paper, we propose a novel methodology for benchmarking and analyzing IIoT devices and applications to uncover insights into their power demands, energy consumption, and performance. To demonstrate this methodology, we develop a comprehensive framework and apply it to study an industrial CPS comprising an educational robotic arm, a conveyor belt, a smart camera, and a compute node. By creating micro-benchmarks and an end-to-end application within this framework, we create an extensive performance and power consumption dataset, which we use to train and analyze ML models for predicting energy usage from features of the application and the CPS system. The proposed methodology and framework provide valuable insights into the energy dynamics of industrial CPS, offering practical implications for researchers and practitioners aiming to enhance the efficiency and sustainability of IIoT-driven automation.