Why did the Sega Game Gear suck so much battery power?
Solution 1:
According to Wikipedia: "[Game Boy's] monochrome screen, lack of a backlight, and less powerful hardware" is at the root of the problem.
Solution 2:
The poor battery life on the Sega Game Gear is caused by the backlight in the screen. It is a fluorescent tube which eats the batteries up at a rapid rate. Recently several people have experimented with replacing the fluorescent tube with LEDs, this dramatically increases the battery life, thus proving that the main power drain comes from the back light.