There are a few schools of thought as to what good burnt ends should be like.
The two most common differences are the slightly larger and somewhat fatty burnt ends that can be easily made by chopping up the point, reseasoning, recooking and saucing. These can range anywhere from crispy on the outside and tender inside, to tender throughout depending on how you make them. In this case, what people are going for is the "point fat" which is quite flavorful.
The other kind is basically the "original" burnt ends, which are literally the bits trimmed of to square the brisket for slicing and/or the bits left of the board that fell of from slicing, usually on the ends of the slices which were most done and fell off. These are usually more trim pieces of meat, not necessarily all that fatty, and are crispy by default due to the nature of how they were created essentially...they are bark-heavy.
I tend to like the original kinds, but I also make these from the point, and some do it this way but most folks making burnt ends from the point do it per the first method I described.
What I like to do is trim all visible exterior fat from the point meat before chopping. This will allow for more "crispy". Then I chop the meat into smaller bits, I prefer really small like 1/2" to 3/4" cubes. I season these, season heavily in fact, and return to the pit for a good 2 to 3 hours to get crispy. I season again at the end with a light dusting for added flavor. I actually like mine without sauce. I like the crispy exterior, the chewy to tender interior, and all that barky flavor. If I add sauce, it is when serving. Like Wampus described above, all this added seasoning makes them a tad salty, but I like mine that way. They're like some sort of BBQ Brisket jerky treats in my opinion...and jerky is salty.
I don't honestly hear of a lot of folks making them that way like I like, however. It is certainly easier to just do the first method I described, and it is by far the most popular.