The model 12 and the model 15 are both adjustable sight guns. The model 11 and 14 are fixed sight guns. The models 11 & 12 used a porkchop barrel shroud and the external retaining nut. The models 14 & 15 used a porkchop barrel shroud with an internal nut. The models 14-2 & 15-2 use the modern, straight shroud with an internal nut.
You will therefore need a model 15 porkchop barrel/shroud/nut for your model 12 if the goal is to have a 4" barrel with a "prettier" profile. A model 15 porkchop barrel/shroud/nut combination will fit on your gun but one from a model 15-2 will not. As noted above the model 15-2 does not use porkchop barrels and the barrel shroud locating pin is in a different location on the 15-2's.
The model 15 is in essence a transitional model between the model 12 and the model 15-2. The important thing is to make sure the shroud, barrel, and nut are correct, relative to each other, on any barrel you buy. By this I mean that it is possible to find porkchop barrels and shrouds in different lengths. For example, Dan Wesson (and High Standard) made both 3-3/4" barrels and 4" barrels. If you try to mix and match then you will find that it is not possible to mount a 4" barrel in a 3-3/4" shroud, or vice-versa. The same applies to 6" barrels. You can find them in both 5-3/4" and 6" lengths. In fact, if you want to put a model 15 barrel/shroud/nut on your model 12 then you are much more likely to find a 3-3/4" barrel than a 4". If that's not an issue then run with it.
Additionally, if you buy a barrel/shroud/nut combination designed for a model 11 or model 14 then it will fit OK but the front sight will be too low since the models 11 and 14 have fixed sights and the gun will shoot too high.
The bottom line is that you can get a 3-3/4" or 4" barrel for your model 12 that will mount up properly and shoot to point of aim, but you have to know what you're buying in order to be happy with the outcome.
-Lee
