I raise both and feel they have very different strengths in some ways, and also a lot of overlap, so it depends on your goals which (or both) will be more appropriate. Both can be great for eggs and meat, but their differences really come out in applied management. They change succession in different ways. If you want a moist high OM area (think elderberry, mulberry, wet woodland crops,) ducks are great. Chickens tend to desiccate/dry an area with their constant scratching (oxidizing) and highly reducing manure. This is perfect for reducing and quickly processing compost. I prefer chickens for establishing an area (disturbance) and ducks for maintaining a large planting, especially in a forest garden scenario. I place the duck house in a sacrifice lot that is deeply mulched, and preferably uphill from planting blocks to trickle nutrition downhill. This area doubles as a holding pen for when a multi inch rain comes to prevent them from going on a rampage. You can either move the area eventually, add more mulch, or muck it out and put it in the compost pile/on perennial plantings.
Ducks:
-Pros
Excellent foragers, not picky about any bugs that I've seen. They will clear any area of any bug they can find.
Less destructive of yard/pasture (but still somewhat destructive if not managed.)
Hilarious - they always seem so upbeat. Entertainment value can't be overstated.
Easy to herd if you understand their flocking.
Reliable egg laying + reliable laying time. My Welsh Harlequins and Campbell are more productive than any chicken I have, including hybrid layers.
Cooler manure, much less likely to burn out grass and other plantings. Better for food forest/orchard settings in my experience
-Cons
Dabble any standing water, they will put ruts in your yard if you get much rain. I prefer this as it improves water infiltration.
Mallard types can be loud, possibly more so than chickens but I'd say it's comparable.
More difficult to process if you're looking for meat.
Mallard types are unreliable for brooding; muscovies are excellent.
Chickens:
-Pros
The best composters. I prefer to put mine on super deep wood chip mulch, innoculate it KNF style, and let them "prep" an area for future planting.
Highly rich manure, excellent for composting and using in vegetable gardens in my experience.
Much better in a confinement scenario (composting in my case,) I wouldn't confine ducks.
Some breeds brood prolifically.
Easy to process for meat.
-Cons
Can be difficult to round up if free ranging and not socialized. Best to train them to a call.
Can be damaging in too small of a yard/pasture.
Roosters can be dangerous if you don't assert your dominance early.
Much more aggressive flock dynamic - sick chickens will have to be removed and protected while they recover if they get too weak.