As has been said here a number of places in the thread, shot stringing would seem to be the biggest difference. And logically, a 12 bore with a higher payload simply has to put more pellets on target. Or at least we are lead to believe. And has also been said here, much has changed in choke tubes and shotgun shells over the years.
My first shotgun was a Stevens side by side 20 ga. Not to date myself, but, in those days the shells were made of paper/cardboard. Plastics had not entered the picture yet. With that shotgun I shot squirrels, doves, raccoons, rabbits, pheasants, ducks, geese, and even deer with slugs. Being honest, I never felt undergunned, and if I didn't bring home 23 critters to eat out of a box of 25 shells I felt I was doing rather poorly.
Fast forward to a few decades later. The firearms industry has done a remarkable job in getting us hunters to believe that critters have become smarter, more weary, are more difficult to kill. The 16 ga fades from the scene and the 12 bore dominates. With the advent of steel shot after a Loon or two ate a lead fishing sinker and rolled a seven, we were wounding a lot of ducks that would have been stone dead had we been still able to use lead shot.
Not to be left wounding ducks and geese, the gun industry rebirths the 10 bore. And just like magic ducks and geese started to die proper again. 10 Bore sales went up, 12 bore sales started to drop. Taking a hard look at the numbers, the gun industry decides it's time to change things a bit and out comes non other than the 12 ga 3 1/2" Magnum. Capable of equaling the now revered 10 Bore.
There are some problems with this right out of the gate. Shot stringing is one of them. The other issue is the weight of the guns being offered in the new and mighty 3 1/2" chambers. While almost if not all 10 bore guns tip the scales at 10 pounds or better, the new 3 1/2" 12 bores are on frames that were designed for 3" fodder and thus weighed to the light side to be firing 10 bore loads. This resulted in getting one's cranial fluid smashed against their skulls and many a bruised shoulder. If one wants to experience severe pain they need only to fire off a few 3 1/2" "Hoss" loads out of a Messberg Ultimag. And if that does not bring tears to your eyes then try lighting up a few of those 2+ ounce Turkey loads. Flinching is no longer just a rifle thing cause.
While the thread is 20 ga vs 12 ga I felt the 10 bore thing needed to get in the picture because to a degree it helps explain the metrics of shot stringing. If we follow the advice of patterning your shotgun (which by the way IMHO IS sound advice) we can get a visual of what the cloud of pellets looks like at various distances. This is indeed wonderful. ON STATIC TARGETS. It makes little difference to a turkey whether all of the pellets crush his skull on impact, or, 30% of the pellets arrive 3 milliseconds later. He is indeed a dead bird.
Let's assume that you have patterned Ole Betsy at say 40 yards. The standard for such things. And you bear a huge smile as you walk up to the pattern board and discover that it has more holes than the business end of a salt shaker. And, even better, they're ALL in that magical 30 inch circle just like the script says. Man it just don't get any better. And it won't, so long as you just shoot at static game.
In order to get a true picture of what goes on in the wing shooting game, one must MOVE the pattern board at the speed of the game being hunted, and the distance it is hunted at. Think about this for a minute. A mallard duck at say30 yards, flying left to right at 25 miles an hour, while you move the gun what you consider to be the proper lead, and KEEP THE GUN MOVING, and finally hit the trigger. You'll soon discover that your juicy perfect pattern is quite oblong and shaped more like a football. If you are one of the more gifted wingshooters you just may have killed that duck.
But like most average shooters, a good string of misses or cripples gets the gray matter working. Ah, not enough pellets to get er done. Well true to a degree if you are fringing them. So let's move up the payload, move up in bore size. Just throw more at em and something good is bound to happen. Right? And the ammo companies are the recipients of the good as you drop more cash to punch holes in the air.
And to make matters even worse, shot shell technology has evolved so that ducks and geese can be killed stone dead out to 70 yards with the right choke combination. Uh Huh. I want to meet that man that can do that on a regular basis, not the lucky pellet on occasion one either. Assuming that this is a possible feat, one has to imagine what the picture looks like as an unseen duck pops in at 20 yards right in front of said duck hunter. If, he is capable of hitting that duck with a 30-06 rifle he will probably kill it with the shotgun as well. That's about what the pattern diameter will be with the high tech shells and super whammie choke tube.
IMO, the industry has gone to far. Consult any worthy after market choke company. They'll tell you right up front, don't exceed 1500 fps velocity, NOT to be used with Federal's Flight Control Wads. Do NOT use ported choke tubes with Hex Blindside or Flying Saucer Black Cloud shells. Don't use anything larger than BB...... And the list goes on. It gets to a point where you don't know which tube to use what shell. Well I know of no one that has gotten blown up by any of the DON'T infractions, you can rest assured that the patterns are blown.
I think old ideas die hard with us hunters. Well, at least they do for me. Early last Fall I happened to be in my local Gun Shop and chanced upon a Benelli SBE. It was a used gun in mint condition and the chap that owned it needed $700 Frogskins for it. I couldn't write out a check fast enough.
Since most, no, all of my duck and goose hunting over the past 10 years has been with a Browning BPS 10 bore I figured to be in the game I needed to be shooting 3 1/2" shells to stay in the game. Ho Boy, WAY off base. Sure, shot stringing played into it, but moreso the brutal recoil going from a 10 pound gun to a 7 pound gun firing basically the same payloads. I did some wicked missing there for a spell. The great lightbulb went off when I managed to scratch down a Black Duck and it was flopping around about 40 yards out on the water. Leveled off and cut loose. And a LINE, not a pattern went straight out to that duck. I might as well have been shooting a rifle.
I pulled out the Mod tube and put in the Imp Cyl and dropped down to 3" 1 3/8 ounces of No4 Steel. And just like magic, the next flock of Mallards that came in, 3 of them didn't leave.
So, in the study of 20 vs 12 bore, vs 10 bore vs about anything. The thing to keep in mind is a rifle is a rifle firing a single projectile. A shotgun is designed to fire a number of pellets in somewhat of a spread to allow for human error and still hit. When the shotgun becomes as critical as to have to AIM it rather than POINT it I do believe it makes little differenace as to the gauge. It's gonna result in a miss if we shoot a shotgun as it was intended way back when.
And that's my 2 cents worth on the subject ;D