As I understand it (and please, I'm no expert...) the internal flash merely tells the external strobe when to switch "on" and "off," in order to send the desired amount of light into the camera's sensor.
Therefore, increasing the strobe's brightness, would require a shorter "on" time to reach the same level of exposure- saving your camera's battery.
Similarly, reducing the photo's exposure level via the camera's exposure and/or flash compensation would result in less light required, and therefore a shorter "on" time- again, less strain on the camera's battery. Overdoing this would however result in under-exposed photo's...