If you are thinking about a Stoeger (or IGA whatever) coach gun, I would consider getting the 12 ga, maybe with the removable chokes. The 20 ga is barely lighter than the 12 ga (built on the same frame) and if you reload you can make 12 ga 7/8-1 oz loads (if you are concerned with meat damage) up to 3" magnums for Turkey (assuming you get the model with the screw in chokes). Would also be a good gun for pushing deer.
I had a friend who had a coachgun in 20 ga, it was a REALLY nice pointing gun, would be great for grouse, but it weighs nearly as much as a 12 ga ( a few oz's I think)
If the 20 ga was built on a true 20 ga frame that would be the gun to have (IMO if they built them on a true 20 ga frame they wouldn't be able to make enough of them), but since you are getting the 12 ga frame you might as well get 12 ga versatility.
that is the gun that I will eventually buy