less recoil . . .
Less recoil is simple physics, The 00 buckshot muzzle velocity of each, .410, 20ga, and 12ga is relatively the same, but as you increase gauge you increase the combined weight of the shot/pellets. It goes something like "for every action there is an equal and opposite reaction". It takes a lot more power, a lot bigger BANG to move the 15 00buckshot pellets out of a 12ga 3" shell at +/-1100fps than it does to move the 3 00buckshot pellets out of a .410.
For a simple, non-gun demonstration get some golf balls and zip-lock bags. Fill one zip-lock with 3 golf balls to represent the .410, one with 9 balls for the 20ga and one with 15 to represent a 12ga 3" mag. Now try throwing the bags at a target - - golf balls or buckshot, it is all relative and all kind of variables can affect felt recoil, but the 12ga kicks harder, because it takes roughly 5 times the power/force to move 5 times the weight of the 3 00buckshot the .410 is pushing, at a similar velocity.
For hunting large game have you thought about using slugs?