Shotgun shell ounce size question

Generally speaking, Shot pattern density. A 1 1/4 ounce load of shot is likely to produce a denser pattern than a 1 ounce load of equal shot size.
This usually translates into the ability to put more pellets on a target, such as ducks, at a greater distance than the lighter weight load.
More drams of powder are also used to propel the heavier load at an adequate velocity.
The down side off denser pattern is that closer shots often lead to mutilations of the target or misses. More shot and powder also means more recoil.

Good points! It's been a real long time since I duck hunted. My comments were based on lead shot.
Even with lead, bigger and heavier isn't always better.