The OP referred to game shooting, not normally a heading that geese come under, and therefore the benefits that a 12b brings to the shooting of heavy steel loads are largely moot. Using extremes to compare anything is not going to provide a particularly balanced outcome. Using that line of logic one could argue that a big 8b is better than all the rest because you can shoot REALLY heavy cartridges through that...
In terms of driven, or walked up, shooting the 20b is every inch the killer that a 12b is. Talk of professional and competitive clay shooters or 3.5" steel loads for geese is meaningless.
On a 60yd cock pheasant in January a seasoned gun will kill it just as dead with a 20b as they would with a 12b. I know this for a fact because I see it done countless times a season.