Can you get ahold of a copy of Storey's guide to ducks? he puts it well.
 
As with chickens their are pro's & con's. Ducks are good foragers, they don't dig either BUT they adore water and water brings mud, so they definitely win the prize for messier, as well unless you go with bantam breeds they require more room.
 
I also think most breeds do better with either quite large areas or free ranging, they don't confine as well as some chicken breeds can. They eat more too, to get proper waterfowl feed can be tricky.
 
All that said, they are less prone to disease, as Storey's guide says, provided with, bathing water,  a clean,  a well fed environment usually health issues are minimal.
 
Their eggs can be sold for more, they are harder to get, rarely can one just go to the store for a duck egg, they make good baking products and are alternatives for those allergic to chicken eggs.
 
I have both but am mainly ducks, i think it more depends on your purpose than anything else, plus each breed offers a few different things that may make it more worthwhile or not lol
 
Ducks can be kept with chickens but some cautions, one as young their feed needs are different, so i would suggest reading over
https://www.backyardchickens.com/t/750869/raising-and-caring-for-ducklings#post_10611711
 
as well if you get any drakes(male ducks) you must be careful they don't try to mate with them, a hen can be lost from this. I would also recommend at least a pair, so the duck can share it's ducky ways vs being alone. The mess the ducks make of an area maybe not be the ideal environment for the chickens either. Mine are not housed nor run together, this means each others needs are met vs compromising.