While they are similar, "Fish in a barrel" tends more towards the mindset of the predator: many opportunities for easy gain.
"Sitting ducks" tends more towards mindset of the prey: they are unaware that they are being stalked.
EDIT: Added Calvin and Hobbes comic strip
Calvin can say that dropping a snowball on Susie is "like shooting fish in a barrel" because it's both easy for him to target her and difficult for him to miss her. This is the predator's point of view.
Before Calvin drops the snowball, Calvin (and the reader) would call Susie "a sitting duck." However, Susie does not know that she is vulnerable at this stage. She could not say, "I'm a sitting duck." Nor could she say, "I'm a fish in a barrel."