Geese aren't friendly unless you raise them from chicks, then they won't let you go. I've never met a goose I could pet, and got plenty of bites and tongue-hisses. Ducks are smaller and cute. They are more skittish, though they will get used to a safe friendly presence. Ducks have tastier eggs. Geese will taste you if you try to take an egg. I once had a pet chicken that would sit in my lap and be petted but now "they" say not to make pets of chickens because of salmonella...
They are both pretty filthy. Neither are really friendly. But ducks don't go after you like some geese do. We have call ducks and they are about perfect in my mind! Small, cute, nice and very independent. Also in the winter they do ok with just a dish of water and not a whole pond.