Here are some of the factors that go into making a generator with wire and moving magnets.
You want the magnet path to be perpendicular to the wire
You want to avoid cancellation by ensuring that the two "legs" of the coil never see the same magnet pole at the same time
You want to maximize voltage by ensuring that the two legs DO see opposite poles at the same time (one leg seeing a north pole while the other sees a south)
You want as many turns as needed to achieve the desired voltage/rpm.
You want the thickest wire you can fit to minimize resistance.
You want the thickness of the stator (for air core axials) to be as thin as possible to have maximum flux between the rotors.
When you add these to the various shapes of available magnets, you end up with a variety of coil shapes each with its own set of compromises.
Hope this helps