When cooking at home, its the same here as Austrailia. BBQ "restaurants" usually slow cook meats for hours in a large smoker. Beef brisket is usually the preferred meat in Texas but other types are also served. A lot of folks in Texas, like me, have their own smaller smokers. Chicago BBQ must have something to do with Upton Sinclair's "The Jungle."

There are different styles and meat preferences across the US. Here's a link that might help:

http://en.wikipedia.org/wiki/BBQ