Old time black powder shotguns are pussycats compared to modern nitro-powder ones. ( more accurate term than smokeless) After a little searching I found my Barnes Catridge book, (it was in the bathroom). I wanted to double check and I was even right.
4 gauge 4" case 3 oz shot max
8 gauge 3-3 1/4" case 2 oz shot
10 gauge 2 7/8" case 1 1/4 oz shot
12 gauge 2 5/8-2 3/4" case 1 1/4 oz shot
The 12 was often used with 1 oz shot for hunting. The 10 gauge will pattern better with 1 1/4 oz shot than the 12 gauge because of the wider bore and more wadding to cushion the shot.
When loading with black powder the besr results are most often when you load powder to shot equal on a volume basis.
One could load 1 or 1 1/8 oz shot in a 10 gauge very easily by using a longer wad column. If the 10 gauge in question has a Damascus barrel on it the choice shoud be easy, go with the 12 gauge if it has drilled steel barrels.
Damascus steel barrels are made of thousands of welds, in fact they are almost nothing but welding. I know some folks are shooting them again but I would not. (I know a bit about welding and metalurgy) They may be safe, but how would you ever be sure? This is my opinion, others I know have different ones on that. One thought on this, if your Damascus barreled gun blew up and killed someone or hurt them bad how would you stand up in court when they asked you why you shot it. Almost every loading manual and box of shells says not to do it.
Judge I rest my case!