Hi JPK,
I get to hunt Yukon moose and grizzly and black bears quite a lot, having them in my yard at times. I have shot my share of them with a lot of different guns and watched even more shot. I cannot think of anthing that would have much of an advantage on a .577 BPE for big moose or bears. When I was searching for a double rifle for hunting these animals my choice of calibers was first; a .500 NE., second; a .470 NE., and third a .577 BPE or NE. Of course price and availability was more the deciding factor, but I was sure not feeling like I was settling when I found my .577 BPE. I think a good .450 NE. would be great too and also a .500 BPE and similar rounds. The 20 ga. was never on my list.
My friend has a lovely original Westley Richards 12ga. percussion double rifle. I sure would like to see that used on our big moose or bears some day too. In close it should be quite adequate. I have heard of moose taken with 12ga. slugs but not 20ga. I am sure it could be done but it's not a popular choice. There are more 12ga. carried for bear defense than anything else, I have heard of the odd 20ga. usually for a lady or someone with an injury or similar. When you see grizzles walking around your first thought is not, " I could get by with a small gun". They are likely fine, but why take a chance?