Some basic facts about shotguns:
All things being equal, including payload of shot, you get an approximate 7% improvement in pattern consistency by stepping up one gauge. (e.g. 28 gauge to 20 gauge, 20 gauge to 16 gauge, etc)
This fact was so well understood by the British, they even made 2" 12 bore shotguns to provide weight and printability of a 28 gauge with identical payload, but vastly superior patterns.
Another fact of shotguns is that a square load, meaning one where the diameter of the payload and the heigh of the payload are the same, produces far less shot stringing and pellet malformation than a long cylinder of shot. This is why the 3" .410 is such a horrible shotgun shell design because its the most exaggerated shot column of any gauge.
American shotgun marketing teams know nothing of the above, or ignore these facts in an attempt to sell nonsense to consumers. Ergo, the invention of the 3.5" 12 gauge shell. For that matter, even the 2.75" shell.
The Brits designed dedicated "fowling" guns for goose specifically 150 years ago, it was a 10 bore shooting a 2-5/8" shell with 1.25 ounces of shot. Using lead, it would drop them from the sky with authority. I've used such guns for geese with non-toxic bismuth loads and I can report they were far more lethal than my companions shooting 3" 12 bore steel shot.
So indirectly answering your question with facts and experiences above, the jist is that a 10 bore is going to do things better than a 12 bore, all other factors being equal. The longest shotgun shots I've ever taken were with relatively light loads in 2.5" shells going at decent velocity...there were no gaps in the pattern and no shot stringing, therefore it was a far more lethal shot at distance than throwing a 30 yard long rope of shot that the bird can fly through unscathed.
