The thing with the Judge (and others like it) is that it is, as the saying goes, neither fish, nor fowl, nor good red meat!....
The advantage to these guns is that they shoot a commonly available shotgun shell (.410). The problem with these guns is that they shoot a commonly available shotgun shell (.410).
Federal law requires handguns to have rifled barrels. You can shoot regular ammo, or shotshells, it doesn't matter, but the pistol HAS to be rifled. Otherwise it is a "sawed off shotgun" and restricted under the same law as machineguns and silencers.
Another complication is the federal regulation that restricts bore size to essentially .50 caliber and under for rifled arms. Anything larger is considered a "destructive device" and restricted. (there is an exemption for the big bore elephant guns). SO, if it's going to be a handgun, it has to be rifled, and if rifled, it has to be .50 or less, so that pretty much restricts things to the .410.
Now, a .410 pistol has its uses, but its performance suffers compared to a .410 smooth bore. And tis not the velocity loss in a short (pistol) barrel that causes the trouble. IT is the rifling. The rifling spins the shot charge, the way it spins a bullet, which means that the shot charge turns into a "donut" with a hole in the middle (where there is no shot). And, this is noticeable at very close range, too. Most pronounced with bird/snake shot, but it happens with buckshot, too, its just not as easily noticed in the .410 due to the small number of buckshot pellets.
The T/C Contender used a "choke" tube (I call it "the straightener"), a tube screwed onto (or into) the muzzle with straight "rifling", which was intended to counter act the spin from the barrel rifling. It sort of worked, but you could not fire bullet (slugs) though it.
The .45Colt/.410 revolvers don't have anything like this (that I know of, anyway), so they are not the best performers with bird shot that they could be.
.410 slugs make a pretty peppy pistol round, being a 1/4oz slug doing a claimed 1800 fps (3in shell) from a regular shotgun barrel. If we assume reasonable velocity loss due to the handgun length barrel then you have a roughly 110gr slug doing 12-1300fps (estimate, I don't have chrono data) which puts it roughly in the .357 mag range. The 2.5" .410 shell has a 1/5 oz slug (even ligher).
But even though .410 slugs should be turning in some impressive speed for handgun rounds, the slugs are not built the same as JHP bullets, and therefore, their performance as self defense rounds is not going to be the same as a .357 mag, or so I would expect. What this boils down to, as a practical matter is that if you are only going to be getting about .357 performance, if that (from slugs), why carry a gun the size of the Judge???
The .45 Colt is a venerable round with a proven 140 year track record, the only drawback it has in a .45/.410 is the long bullet jump to the rifling. In some guns it doesn't seem to matter much, but in others the long jump to the rifling has a detrimental effect on the accuracy. Unfortunately, you can't know for sure, until you shoot that particular gun. I've read reports of people saying how their Judge was accurate with .45 Colt ammo. I won't dispute them, I'm sure their gun does what they claim. But others might not.
I've got a .45.410 Contender that was reasonably accurate with .45 Colt ammo, but the same ammo in my .45 Colt (only) barrel is more accurate than in the .45/.410 barrel.
.410 buckshot? yeah, some good there, traditionally used against varmints and small predators at short range. Not a deer load, really.
The irksome thing about the Judge, and similar guns, for many of us is the marketing. These guns are being promoted as good self defense guns, relying mainly on two of the big shotgun myths, and most people's lack of understanding of how things really work.
One myth is the tremendous "power" of the shotgun. Blows guys through windows and even almost stops the Terminator. In the movies. The 12ga does have power, but it gets it through mass. The .410 doesn't even come close. But people hear "its a shotgun shell" and think of what the 12ga does.
The other myth is "with a shotgun you don't need to aim", which isn't (and never was) even remotely true. While you may not aim a shotgun like a rifle, if you don't aim, you simply don't hit. And at close range (defensive use) the shotgun pattern hasn't had time to open up much, often not being any larger than your fist, if that, at across the room ranges.
Many people are buying them with greatly inflated expectations.
As a survival gun, they also fall short. While the .410 will do a fair job getting small game to eat, for the size & weight of a Judge and a single box of ammo (25rnds) you can pack a .22LR and a couple HUNDRED rounds of ammo, with just as much effect (when properly aimed) and about double the usable range of the .410.
They are a novelty gun, and as long as you get one with your eyes open, great fun. But if you get one thinking you are getting the best thing for (insert use here), your eyes are not open.
