IMHO, if you have cooked the perfect brisket, then you serve it sliced with the sauce on the side. You want to make sure everyone knows just how perfect that piece of meat is.
If the meat is going to be served gradually over a few hours, leave the fat cap on while the brisket is in a holding oven to help keep it moist. Simply slice off the fat as you slice a serving of meat. You can also trim the fat out of the center of the brisket as you are serving. With a little practice, the slicing and trimming process actually becomes part of the "atmosphere" of your event.
The chopped brisket mixed with sauce is what to do with some of the leftover brisket for the next day. The meat will loose some of its texture if in a walk-in over night, so the restaurants will then make the mixture to disguise this. It is also a way to cover up a less than perfect attempt at smoking the brisket for the day.
At least, that is the preference for this Okie.