What is the difference between a shoebox solar oven and and a pizza box solar oven?

Answer 1

For a solar oven you want to maximize the reflector/collector surface area, (more sunlight=more heat) and minimize the oven volume (less air/stuff to heat up with said heat) to get more rapid heating.

If you are painting the box black, and lining the inside with foil to hold the heat in(or a similar design), the Pizza box has more area exposed to the sun, and since it is thinner probably has the same inside volume as the shoe box.

If you're opening the box and using it as a foil lined lens, the pizza box is again better, as it can gather more sunlight. The shoe box's only advantage is it has the ability to hold a small chicken, but for most cooking purposes the Pizza box is the best option.

Really an "ideal" lens shape (like a satellite dish) would work best to focus the sun on one spot. If you made a foil covered dish, and put a your food at the focal point, this would work the fastest. a Google search on lenses could give more specifics if you go this route.