I'd be curious to start with say, a 30" barrel and take it down 2" at a time until you hit about 18", then take it down inch by inch, all cylinder bore with the same exact shells.
That is the way shotguns were made at one time. And that's when barrel length does become an issue. It is certainly true that chokes make a huge difference now.
Rifled barrels like the Judge has also will greatly affect shot spread. You'll generally see a donut pattern that is much larger than a smooth bore pattern would be. That doesn't mean the Judge isn't an effective SD weapon BTW. A short range blast with a Judge using shot shells is going to hurt whoever it happens to hit. It is certainly going to leave a mark.
But let's not forget the .45 LC shells you can use in a Judge. To me that would be the choice of shells but I go with .45 ACP or .40 for SD myself.