The words 'duplicae model' bother me, because it sounds like it's creating a new model in memory with different texture values, thus adding a fair amount of data that is totally unneccessary.
This is exactly what happens. "Duplicate model" creates a new instance of the original ship model and then reskins it. "Regular" simply switches in the new texture during rendering.
"Regular" worked when it was first released, but at some point early on it stopped working and I haven't gotten around to finding out why. It's possible it has something to do with the HTL upgrade.
The reason for the two modes is for efficiency's sake. "Regular" should be sufficient for most situations, like nameplates, but if you have a whole bunch of textures replaced (like the Orion/Hatshepsut in JAD2) then "Duplicate" might be a better strategy. I've never conducted any benchmark tests, but here are the tradeoffs:
"Regular" pros:
Uses less memory, because it doesn't need to copy the model
"Regular" cons:
Very slightly slower, because it has to do a texture check every time it renders the model. This probably doesn't matter for simple one- or two- texture jobs, but the more textures you replace, the more checking and switching you have to do.
"Duplicate" pros:
There's no slowdown at all during the mission, because once the duplicate model is created, it's rendered exactly in the same manner as an unmodified model
"Duplicate" cons:
Significant increase of memory because of all the model data (an entire polymodel struct) that's copied.