Here are some tips I learned while in Texas visiting some of the great BBQ places around Austin. As PitMaster T has pointed out, there is no difference between the red/brown butcher paper and the white butcher paper. Of the places I visited Snow's wrapped in foil, Franklin, Kreutz, and Smitty's used the red/brown paper while JMeuller used the white paper. Here is a pic of a piece of meat being unwrapped at JMueller's.
One thing about butcher paper is that it's pretty heavy gauge stuff and is stiff. So, to make it more pliable and easier to wrap around meat, I learned that it helps if you ball the paper up a few times before wrapping the meat with it. Just cut as much as you need and ball it up into a ball. Flatten it out again and ball it up again. Do that a few times.
I have gotten to the point where I put a light coat of meat drippings or spray oil on it before I ball it up then I just let it sit balled up until I need it. This makes the paper much more easy to work with.
Here is a pic of a BP wrapped chucky. When you wrap, make sure the last fold is on the bottom so the weight of the meat can hold it in place.
And, BTW, this time of year, don't forget to save some treats for the Q monster!
I got to talk with Stacy Franklin about how their BBQ is cooked. She told me, among other things, that they wrap mainly to protect the bark while the briskets are all stacked upon each other in the cooker. They wrap near the end of the cook time, stack the briskets upon each other and then they unwrap each brisket as they are served.
Here is a pic of the chucky after a 1 hour rest. Notice how the paper is well saturated with juices from the meat. This, I believe, helps to keep the meat moist and really does protect the bark.
Here is a pic of the chucky just after it was unwrapped. Notice the great bark. The chucky was rubbed with only salt and pepper.
Thanks for looking!