Duck is typically better tasting, although they are both good when prepared properly. One thing I did that made cooking and eating wild game a LOT easier was set up an outdoor kitchen. Cooking duck inside, especially wild duck can get smelly. Works great for fish too.
Doesn't take much, some masonry block, capstone, tile to face the masonry block... They have some drop in propane burners (grills and stove tops) or you can customize it to a charcoal grill or both, depending on your space.
;o)