Duty-cycled Medium Access Control (MAC) protocols certainly improve the energy efficiency of wireless networks. However, most of these protocols still suffer from severe degrees of overhearing and idle listening. These two issues prevent optimum energy usage, a crucial aspect in energy-constrained wireless networks such as wireless sensor networks (WSNs). Wake-up radio (WuR) systems drastically reduce these problems by completely switching off the nodes' microcontroller unit (MCU) and main radio transceiver until a secondary, extremely low-power receiver is triggered by a particular wireless transmission, the so called wake-up call. Unfortunately, most WuR studies focus on theoretical platforms and/or custom-built simulators. Both these factors reduce the associated usefulness of the obtained results. In this paper, we model and simulate a real, recent, and promising WuR hardware platform developed by the authors. The simulation model uses time and energy consumption values obtained in the laboratory and does not rely on custom-built simulation engines, but rather on the OMNET++ simulator. The performance of the WuR platform is compared to four of the most well-known and widely employed MAC protocols for WSN under three real-world network deployments. The paper demonstrates how the use of our WuR platform presents numerous benefits in several areas, from energy efficiency and latency to packet delivery ratio and applicability, and provides the essential information for serious consideration of switching duty-cycled MAC-based networks to WuR.