Mash is a very traditional approach, a ground up mix of ingredients, which can be fed wet or dry. Pellets are really the same product just steamed and pressed into tiny pieces.
Pellets are the most convenient to use and they flow through the feeders easily assuming that they are kept dry. This is why we recommend feeders to be kept under cover in the chickens coop hanging from the ceiling or rose off the coop floor onto blocks. Giving pellets ensures that the chicken is getting goodness in every piece of food and not selectively eating.
Mash is cheaper to buy in large quantities. It takes longer to eat which is why its good for bored birds mostly commercially reared. Waste levels are higher though due to more dust.