Chickens or ducks for a small garden that floods every winter?

Politely disagreeing with the top answer, because I think the species is the wrong variable here. Your problem is that the ground holds water for four months, and ducks on saturated clay will give you a bog with birds standing in it. I would fix the ground first: lift the run, put down a geotextile membrane and 100mm of angular gravel, then hens on deep litter over the top. That is where your 400 should go, and it works for whichever bird you end up with.

I have five hens and three Khaki Campbells on similar clay, so I can give you the honest version. The ducks genuinely do not care about the wet and mine laid straight through two winters where the hens stopped in November. What nobody tells you is that ducks turn water into slurry: whatever you give them to dip their heads in becomes brown soup within a day, and they will find the one soft patch of lawn and puddle it into a wallow. Hens wreck borders by dust bathing, which is annoying but dry. On the kids, my hens will sit on a lap and the ducks scream if you so much as reach for them.

Numbers from my own book, because the breed pages oversell both. My three Campbells gave me 611 eggs between them last year and did not stop for winter. My four hybrid hens gave 742 but took about ten weeks off between November and January, so the annual totals are closer than the winter experience feels. Duck eggs are bigger and much richer, which is brilliant in cake and divisive on toast, and I could not give them away locally at first. Feed cost was within a few pounds of each other over the year, so pick on temperament and mess, not economics.

Kids plus ducks is the part I would weight heaviest. Ducks do not want to be held and never will, and a child who wants a pet gets a bird that runs away for ten years. Get hens, get docile hybrids, and put the money into the run base.

I did exactly what you are considering and got ducks specifically because of the wet. Two winters later I had a bog with a fence round it, the smell in February was genuinely unpleasant, and I ended up spending another 180 on membrane and gravel that I should have spent at the start. The ducks were fine and happy the whole time, which is the frustrating part, they simply do not mind living in what I had to clean up.