Swamp Collie - Probably the issue is related to the ballistic coefficient of the "fatter" slug of the 12 guage. It is not as good as a typical 20 ga. sabot.
I have shot both a 20 ga. and 12 ga. set up for use with sabots. But only at the range. I sighted both dead on at 100 yards. Then tried both at 50 and 150. The drop of the 12 ga. at 150 was about 2" more than the 20 ga. Not sure that even matters in the field. At least where I hunt, for shots seldom exceed 100 yards.
Groups out of both were really good. Both were Reminton 870's with the Remington rifled barrel, using Remington 3" shot shells. There is no doubt that the recoil of the 20 was less, but again, for me not enough to matter. If I were to hunt with such a set-up, after what I saw at the range, I would go with a 20 ga. simply because it felt lighter, especially with a full magazine.
The two folks that hunt with these two have killed many, many deer .... some out as far as about 135 yards.