In theory they are more efficient.
Throughout the pedal stroke your leg doesn't give an equal amount of force - ideally you want to spend most of the time pushing down with the big thigh muscles and a minimum time in the horizontal movements at the top and bottom of the stroke.
Elliptical front cogs give you a more up-down leg motion, so more time with the big muscles and more power - not sure how much it actually works in practice, or how much practice it takes to make it work.