Korky adjusts the balance of bowl to tank fill rates to Toto's specifications to ensure very little water goes down the drain and the bowl and tank both fill up at the same time. From what I've read, the generic version fills the tank faster and the bowl will be deficient. This will lead to a bad flush, since it doesn't start with the right amount of water in the bowl. They substitute a different restrictor to force more water to the bowl (by slowing the fill rate to the tank), and when the tank is full, so is the bowl.
You might be able to extract the restrictor from an old one and put it in the generic valve to customize it.