From a culinary standpoint, ducks and geese are more like beef than chicken. They *must* be served either rare-to-medium or gently (emphasis on gently) simmered for hours.
I do not bleed out my ducks nor do I soak them in brine. I hunt ducks in California, where most are naturally very fatty to begin with (I can render out 1/4 cup of pure fat from a mallard!) If your ducks are not fatty, bard them by laying smoky bacon on top. If you don't want smoky, cut very thin slivers of pork fatback (in the meat section of your supermarket) and do the same thing. I say this because some people brine their ducks to make them more tender, but you need not brine a skinny bird if you lay fat on the breast, like a pheasant. Brining a duck is a bad idea, IMHO, because most ducks are tender anyway served rare-to-medium. And the blood in the meat is a HUGE part of perfect duck flavor.
Geese are a totally different matter. Geese are 1) big, 2) likely to be older, which means tougher. (how old is your bird? feel the keel bone, which separates the two halves of the breast, and if it is pliable you have a young bird. If it is rigid, it's mature-to-old) I *would* brine a goose, but be sure to put spices/herbs of your choice in the brine as a tradeoff to losing the blood, which will seep out of the meat as it brines. Geese, like ducks, need to be served medium-to-rare. (unless you crock-pot them or make jerky) Geese also make AMAZING sausage mixed with fat taken from a domestic goose or pork fat.
OK, OK, I could go on for hours. (I was a professional cook) But hopefully this will help. PM me if you have any questions.
I love all of God's creatures, properly prepared.