Hey Robert,
Fairly recently, I commented about the weight in 12 gauge barrels and as I remember it's maybe a 2 oz. per inch or so but I'd have to check to make sure.
Gun for gun, there's about 1 pound of difference in weight between the 12 and the 20.
I also find that the shells make quite a difference. If you just look at the shot weight alone, 20 gauge shells at 1.25 oz. and 12 gauge shells at 2 oz. the 12s would add 2.25 oz..f or 3 shells, in the shot payload alone.
So, if you compare guns of equal barrel length, the 20 fully loaded might be one pound and 2.25 oz. less than the 12 gauge.
Thanks,
Clark