Geese are better for weeding, but ducks are better for pest control. And I can say absolutely that they are WONDERFUL at pest control. Both ducks & geese must be fenced out of the garden when the plants are young. Geese can take out a row of lettuce in no time flat, and ducks will dig up sprouted seeds and make a quick meal out of them. But for mature plantings and/or fallow gardens, they are superb. Also, for pest control, the ducks don't actually have to be IN the garden full time--the fact that they are foraging nearby & AROUND the garden will significantly reduce populations of pests.
In other good news, you can raise ducks and geese together and have a small mixed flock to perform both functions PLUS adding natural fertilizer as they go.
Geese also provide a good advance warning system and a low level of predator protection for the ducks. Still need to fence them in at night, because even a goose is no match for a determined predator, but it is still a help. Geese are also smarter than ducks and will make intelligent decisions when something goes wrong--for instance, I had a duck get tangled in fishing line at the community pond. If it had been a flock of ducks, they probably all would have hung around her offering advice and support all afternoon. Because they have a goose in the flock, the goose & the tangled duck came running up to the backyard looking for someone with opposable thumbs to fix the issue. Then the goose settled the duck into her pen & went back to the pond to round up the rest of the flock.
Good luck. If space is an issue, you can raise maybe one goose and two ducks together, and they'll make a fine grouping and good little garden patrol. If you choose good egg laying ducks, they'll provide that nice little bonus too.