Digestive upset can happen in chickens with abrupt diet changes, but they tend to be milder when/if they occur. I think this is because of two main reasons:
1) While the different diets may differ in ingredients, the overall macronutrient composition (protein, carbs, fats) tends to remain very similar. Dog/cat food varies tremendously in its composition so their digestive systems may have to up/down regulate the production of certain enzymes and digestive aids to handle the new food...there is a lag while everything readjusts and during this lag not only can improperly digested food components draw water into the gut on their own, they can also severely upset the established gut microflora.
2) Chickens have well-developed ceca designed to create an ideal environment for the growth and reproduction of those beneficial bacteria to ferment the food for the chicken. The colon is constantly reseeded with this reservoir of good bacteria via "cecal poops". The cecum of a dog or cat is much more rudimentary and more susceptible to imbalances.
