Kevin,
We barbecue pork, but grill beef.
A pork shoulder is put on the pit around midnight, 2:00 a.m. at the latest. It is basted with the sauce periodically and smoked over hickory and oak wood and kept away from the fire, letting the meat cook in the smokebox. It is then taken out around around 9:00 a.m. and the meat pulled from the shoulder. It is chopped just as it is served, and additional sauce added. I prefer the sauce made with red peppers.
Beef, on the other hand, is cooked on a grill, over the fire with generally high temperatures. It should be done through the center but still retain the juices. Beef should be cooked with a blend of mesquite wood and oak.
We do have steak houses in Memphis, but no barbecued beef. I have seen some advertising brisket, but these places generally cater to tourists, or those who may be transplants.
Bob Wright