These birds will eat just about anything, especially if there is little for them to eat. Chickens will destroy small plants and seedlings with their scratching and are even useful for weeding around larger plants such as hostas. On the other hand, ducks would relish hostas.
There is a question about chicken wire being as useful for keeping those birds out of gardens as well as keeping them penned in. Fencing them out of your perennial garden may well be the safest way to go. But realize that certain varieties of these birds may be good fliers, and fencing may have only limited utility.
