Eat both, but I would prefer duck because they eat algae, and generally animal matter coming from an 'aquatic food source' has better nutrients than animals fed grain.
Check out some of the chicken threads we have had lately, we all agree that chickens should be fed grass fed meat and insects, but they are usually fed grain (even when they are pastured).
Find out whether the ducks are given much grain or if they mostly eat pond-matter, and compare it to the chickens, then you will know if picking duck over chicken often is worth it.