This stuff is expensive, but it DOES work. I have it on a wall between layers of sheetrock...which is what you'll have to do if you want it to hang correctly. It's a bitch to work with because of it's weight (you'll need at least two guys to install it) and you'll want to make all your cuts before you hang it, but it's worth the work. Of course, if you have a door on that same wall going into the house, you'll need to do some extensive work on that also, otherwise it'll be a bit of a waste installing sheetblock.
My install is on one half of a double wall system (from outside layer to outside layer goes like this: 5/8" sheetrock -layer of sheetblock -5/8" sheetrock - metal studs with 3" mineral wool - 6" space - metal studs with 3" mineral wool - 5/8" sheetrock - 5/8" sheetrock). These walls are between my control room and my tracking room and each wall has a door and a 4'x8' window. I get a miniscule amount of sound through the doors, but the walls and windows are solid. I'm sure the sheetblock has a lot to do with that.
If you can't get that extreme, you could put the sheetblock over the existing wall and cover that with another layer of sheetrock. I'm sure that will make a significant difference...but you'll still have to work on the door. A lot of sound gets through doors.
So, after all that, my opinion is...go with the sheetblock. It definitely can't hurt. But if you're not going to cover it with sheetrock or do any work to your door, save your money. It's up to you...you know how much money you want to spend and how much work you have to do.
And, I've never used the Auralex brand. I got mine for Silent Source (bought a huge roll of it and still have quite a bit left), but I could drive there and pick it up so I save a boatload on shipping.