The main reason for the difference in cooking time between small and large potatoes (pieces), is that it takes time for the potato to heat up. When a potato is heated from the outside, that heat will slowly have to penetrate throughout the potato. The shortest distance within the potato determines how fast the heat gets in. This is why a long french fry will cook just as quickly as a short french fry, it's the thickness of the fry that limits the heat transfer (of course, assuming that the fry is longer than it is thick!).