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As you say, they are just a type of pedal. The “Eggbeater” is also available in other designs which have a platform around what is the basic Eggbeater.
In my experience of Crank Bros pedals, your feet generally come unclipped themselves in proper crashes – you unclip from this style of pedal by twisting your feet to the side slightly.
Advantages are ease of use, “float” (so your foot can move around a bit whilst still clipped to the pedal, so your knees can get comfy, which is not possible on some other pedal designs), good mud shedding ability, and light weight.
Main disadvantage is reliability, although you will hear conflicting views on that. My Crank Bros pedals have been no more reliable or unreliable than any other bit on my bike. The new 2011 range is supposed to be more reliable.