A simple, but largely ineffective solution is to use 2x6 headers and sills, and 2x4 studs 16" o.c., with the studs alternating facing one side then other side of the wall, so that there are no studs connecting the two drywall faces of the wall.
My experience has been that simply adding insulation to a conventionally-framed wall won't help very much -- the framing itself is a great sound conductor. The good news is that with today's trend to installing home theaters, there's a lot of interest in, and a lot of vendors selling, acoustic insulating products. The bad news is that they're pretty pricey.
If you're serious about this, though, contact any high-end audio showroom, or spend some quality time with Google. I've seen such "room-within-a-room" installations and the sound reduction is, indeed, dramatic, but as I said, the cost is also.
To answer your question, there's probably no difference -- Kraft-faced or not. Neither one will work very well.