Different types have different advantages and disadvantages.
Slot can be opened with stuff that isn't screwdrivers (keys, coins, etc). They can take more torque than Phillips and are cheap to make. They kind of suck to use though, the screwdriver/bit likes to slip off.
Phillips self-centers the bit, and is pretty tolerant of wrong-sized driver for the screw. It strips easily though.
Torx, square and Allen are more expensive to make and require the correct size driver, but they're higher torque and the driver doesn't slip out of the screw.