A voltage regulator, such as the LM7808, provides a stable output voltage and is better suited for powering devices like an Arduino, especially under varying load conditions. In contrast, a zener diode can only clamp voltage to a specific level and is less effective for larger currents, making it less reliable for this application. The discussion highlights that while both components can regulate voltage, the linear regulator offers better stability and protection against overvoltage. Additionally, using a pre-made AC adapter is suggested as a simpler and safer alternative to building a custom power supply. Ultimately, for consistent performance and safety, a voltage regulator is recommended over a zener diode for this circuit design.