Both guns will serve you for duck ... if needed, but I'd tell you to take the Model 12 out the first 3 times you go duck hunting. I think you'll find with different types of hunting ammo you can hunt ducks, deer, grouse, rabbits, woodcock, squirrels ... the list is endless, ....
All you would really need is another Model 12 in 16 gauge. Wish I had one in 16.
The Mossberg, if in good condition, will last several lifetimes. 20 gauge is a very nice starter shotgun for smaller framed folks, but fit is more important than poke.
I have one of each (or nearly the same) of the 2 guns you received from your grandfather. I'm sure you'll enjoy them.