What's obvious on reflection, if not immediately, is that foot-powered kayaks use an entirely different muscle group to power them than traditional kayaks do. Most of the differences between the pedal and paddle experiences arise from this clear difference, but some of the complexities may surprise you.
Foot-powered kayaks are moved through the water, to put it simply, by transferring the movement of your feet and legs to fins -- also called sails -- beneath the vessel. Your lower limbs are doing the rowing in this case, and usually replicating the classic oar-stroke of a paddle in order to do it. If you think about it in terms of physics, you're just using a simple machine to transfer one movement -- pedaling -- back into the original form, paddling.
Advocates of foot-powered kayaks will point out that you already use your feet and legs for locomotion -- and most people don't use their arms this way -- and contain larger, stronger muscle groups intended for that purpose. But that's not the whole story, either. Imagine bicycling, for example: You use your legs to pump the pedals, just as with a foot-powered kayak, but you're only working against gravity in that case. The force you're expending goes downward, for the back half of each revolution, raising your body at the same time you're pushing down the pedal.
Not so with a foot-powered kayak. To power the pedals in this recumbent position, you're pushing backwards, not down. While there are ergonomic benefits here -- less downward pressure on joints and feet means less stress on them -- you're also bringing your lower back into the mix, as it presses back against your seat. This, some say, can result in repetitive-stress and sciatic complications due to the different movements involved.