You should ALWAYS offer the same prey type than what was previously fed to a new animal, switching is never the priority.
You will get better success switching a well established animal that is eating for you than one that is not, and when you switch you go from one prey type to another, than f/t or the opposite but you do one step at the time.
Note: Feeding mice to an animal that eats rats is kind of a step backward IMO, get the animal to eat and than switch to F/T rats if rat was already what the animal was eating.