I’ve never shot a Taurus Judge, but in the past I’ve researched it and read that it does shoot both BUT it doesn’t do a good job with either caliber.
In any case, the best gun for the job is the one you have, not the one you don’t!
I’ve shot it and it does fine. What it does NOT do well is shoot shotgun rounds because it has a rifled barrel [so that it is not classified as a sawed off straightbarrel shotgun].
When you have a short barrel and it’s rifled, it introduces rotational velocity to the shot rounds and they spin outwards faster than ordinary straight-barrel rounds. It’s good for short distances but really bad at anything longer than a few yards.
That is offset by the handiness of having such a versatile street cannon. Basically you can load up snake/shotgun rounds + slugs + PDX rounds all in the same revolver.