The Johnson Martin insulation I used comes in 8' lengths, and essentially is in a double plastic enclosure, with the ends exposed. On the side facing the outside shell of the house, the plastic is very thin, almost see through, and a light color. The plastic facing the interior of the room is thicker, and is what is stapled to the joists.
To be honest, I installed one batt backwards but decided not to turn it around because it would rip trying to get it off the staples. Also, its much better than the paper-backed wool insulation I had originally that was stolen by the mice over the years, so while I probably could have gone after perfection, I was too lazy/in a rush to deal with it.
But to be fair, none of the insulation or paper backing I removed from my structure was wet or damp in any way. The key to this is soffit vents and a ridge vent. I don't have the latter, however I did install soffit vents in the back eave which weren't there initially, one per joist, allowing fresh air to flow in either the front eave or the back eave, and out the other. The front eave only needed two large vents rather tha one per joist, because its a crawl space. The back of the structure just has a soffit at the top edge of the dormer.
I debated cutting into the roof for a ridge vent, but decided it was going to be terribly expensive, and very easy to screw up. For 63 years there were no vents whatsoever in this part of the house, so I figured any venting I do is better than what was there. Also upon exposing the joists, studs etc, nothing was damp, wet, certainly no damage other than mice chewing marks and some carpenter ant damage, all of which has been fixed/replaced as necessary.
Had my roof ridge not been two different roof materials mating at the center, I'd have done the roof ridge vent thing. I even bought the materials and returned them. The front of the house is completely covered in slate, as is the rear, except for the studio dormer at the back, which has a fiberglass sheet roof covered in some goey substance that I have to regoo. its called "Silver seal", if i can find it.
Anyway, I appreciate you wanting to research the vapor barrier types for your studio, in your position I'd do the same thing. Thats why I shared the logic I used so you can see why I made the choices I made. Our situations are different, you're all new stuff whereas my house has been here for 63 years with zero dampness or water damage due to condensation on the insulation. I also had the old insulation rudely relocated by mice, maybe thats why it didn't rot in the joists.
I've read sites that say kraft facing is only a retardant and will eventually fail etc... I've read others that say it just fine to use.