I have hunted both a lot over the years. In the early 90's ND was unreal. In 1994 they issued under 3,000 licenses and by the late 90's they were issuing the max quota of 30,000. The hunting was still good but we had been spoiled by the previous years. We almost exclusively field hunted in ND and permission was not a problem for the most part.
We now hunt SD when we can draw tags and we do most years. I saw a report that stated 3/4 of puddle ducks in North America were in SD at one point last fall. There was so much water and flooded grain, I am surprised every duck was not there. We hunt mostly over water in SD, using waders (no boat necessary). Apply for the licenses in SD and go there if you draw them. Almost anywhere in NE SD is loaded with ducks in late October adn early November depedning on the weather of course.
If you love to jump shoot ducks go somewhere else.
Let me know what you decide and I will be happy to point you to specific areas, especially in ND since I have no plan to return there in the near future.