You sure those weights are the same? The poster didn’t mention that.
Shotgun ballistics are funny, and it took me a while to get my head around them. Speed is not so vital as nominal charge weight. Usually the speed for shot is approximately 1200 FPS no matter the weight, thus you need heavier powder charges (dram equivalent) for heavier charges. The dram equivalent necessary to propel say 1 ounce is the same regardless of the size of pellet (of course once in air, differing size pellets will behave differently, buckshot will carry quite a distance, # 12 only 100 or so feet).
The high speed shells (usually above 1350 FPS) are almost always steel, which requires higher velocities to have the same terminal effects as lead. Given that most birds are taken under 50 yards (never mind Elmer Keith and his claims of geese blown out of the sky at 90 to 100), we have a very limited window of velocity needed depending on shot material.
At 25 yards, there is no difference in velocity and (given the same choke or constriction) pattern size between a .410 and a 12 gauge. The main difference is in pattern density, with # 9 shot having 658 in 1 1/8th ounce and a .410 having 292 in 1/2 ounce.