To elaborate on Matt's answer just a wee bit....
Consider the typical pedal crank driven by the typical rider: virtually all the thrust from each leg occurs when the crank is in the forward 1/3 of its rotation. The top and bottom of the cycle are essentially dead zones. So, with each leg contributing to 1/3 of the cycle, thrust is applied to approxomately 2/3 of the revolution.
With the Ketterman design, each leg applies thrust to a full 1/2 of the "cycle". For that reason alone, you have a 50% improvement in available thrust.
But that's not all. The leg can apply its greatest thrust when it's almost fully extended. Where does that place you on a rotary crank? In the dead zone! With the Mirage drive, however, you're applying your maximum power.
So how do the two systems compare on the water? I happen to own a Waterbike by Seacycle (one of several convential pedal boats on the market). It's a pretty fast bicycle type drive attached to a propeller. The biggest difference in feel is that those dead zones are harder to cycle through with a prop than a bicycle, so your prop is always changing speed. It's not nearly as comfortable to pedal as the Mirage. The result? It hasn't left my garage in three years. Anyone want to buy it?
There are other issues concerning propellers vs. fins. We could compare the systems in terms of weight, simplicity, maintenance, compactness, antifouling qualities and versatility of use, but those aren't topics for today. Suffice it to say that the Mirage drive competes very successfully against other pedal designs.
Matt modestly neglected to mention that Greg Ketterman's Mirage drive has won several design awards. It's probably not too much of an exageration to describe it as a breakthrough comparable to Nikolaus Otto's internal combustion cycle and several of Thomas Edison's inventions. I'll bet most Mirage users have no idea they're driving such an innovative machine! No doubt, when the patents expire, we'll be seeing Ketterman drives applied to all sorts of contraptions! By the way, the Mirage drive is not his only innovation....