Sound proofing and sound deadening really are two separate things. Sound proofing is MUCH more difficult in my experience than sound deadening.
I will say, that one of the nicer solutions to sound deadening was in a home where they put carpet on all the walls. Yes, ALL the walls. Even wrapped a couple of columns in the room with the carpet. It was a low-profile carpet, similar to what is in some offices, but the design on it was nice and complimented the room very well.
I would not say that it did a great job of sound proofing the space though. Deadening, yes, but not proofing. To keep audio from really escaping the room seems to be all about the separation and thickness between adjoining spaces. There are tons of videos and discussions online about this, but it is definitely a case of you get what you pay for with sound proofing. Raised floors, double drywall, staggered stud designs, asphalt sound proofing materials, Green Glue, etc. Even the door to the room needs serious consideration when listening for best results.