In a buckshot load, the standard for 20 gauge is #3 buck, which consists of twenty pellets, each a quarter inch in diameter. Among common 12-gauge shells, the closest would be the so called "urban police load," #4 buck. This consists of 27 pellets, each .23 caliber. Velocity is roughly the same, whether twelve or twenty gauge.
For home defense purposes, let's say two evil twin men are kicking down the front door, announcing their intent to murder every man, woman, and child in the house. Spouse A fires a round of 12-gauge #4 buckshot and sends 27 .23'' diameter pellets into the chest of the first evil twin. Spouse B unleashes a single round of 20 gauge #3 buckshot, blasting 20 .25" diameter pellets at approximately the same velocity into the thorax of the second evil twin, with all the projectiles penetrating to approximately the same depth.
Who's going to know the difference? Only the medical examiner, and then only after he meticulously counts the white spots on the X-rays, or tallies the number of pellets removed from each corpse.