Harmony and Backinwellies hit the nail on the head.
The only thing I'd add is that because hens go to bed of their own accord, you can buy or make an automatic door opener / closer, which then means they only need to be checked once a day, the same as the sheep.
Because ducks and geese need to be herded to bed, somebody needs to be around at dusk to do that, which is not always easy, especially in the winter when you're still at work when it gets dark!
Ducks and geese are indeed hardier than hens. However, as long as you buy 'normal' hens (avoid fancy breeds like silkies which have special requirements) and give them places to shelter from the rain and wind, you'll find they're pretty robust.