Yep thin slices. I bet you had to slice much thicker when warm or hot even.
Not sure if it is really a meat quality issue as much as a technique concern. I think it needs to rest at some point to firm up a bit prior to slicing. Also, a sharp knife without sawing away at the meat- one pass per slice will keep each brisket slice more intact. Depends on doneness too I suppose. At some point the meat loses its cohesiveness beyond the point of unctuously tender and is mushy and crumbly no matter what.