I have both. Let's talk chickens first. I love the colorful egg assortment you can get. They are great for bugs but they scratch up everything. They can turn a beautiful grass area into a pasture of dirt. If you are going to sell eggs, most people prefer to purchase chicken eggs and colored and speckled seem to be all the rage right now. They are entertaining and fun. Now with the arrival of the Bielefelder chicken you can get meat and loads of eggs too. They are super sweet birds.
Now ducks. I love ducks! The sassy way they talk to me when I go to feed them, the way they love water and they can be such clowns. Depending on the breed they can lay as much as chickens. They are superior for slugs and snails. They will eat grass but not tear it up, so far. Here's where my chef training comes out. They are superior for baking. Loftier bread and wonderful cakes. My favorite pumpkin pie is made with them, delicious and creamy. They scramble up beautifully too.
I'll throw one more in the mix as a bonus, quail eggs. I love them, especially pickled and they make beautiful tiny deviled eggs. I have been reading about quail eggs for people with seasonal allergies. They may be on to something. Checkbout the article about the French doctor. The drawback, they are little prima Donna's and things can affect their laying and boy can they eat. They need secure quarters from cats and predators. They are fun and pretty friendly. When they are happy they can really lay.
Since they all gave pros and cons, I couldn't decide and I have all three plus a couple of chatty geese. So good luck to you deciding what you prefer.