With all due deference to the low 'n slow guys, I don't believe that's what hyde is referring to.
Pit beef (found at Chaps, among countless other Baltimore establishments) is the antithesis of low 'n slow... a chunk of beef, maybe lightly seasoned, charred over a fire (rare and medium rare seem to be most popular), sliced thin and served on a kaiser roll with horseradish and onions, tiger sauce or BBQ sauce. Trying to compare and/or stratify the virtues and relative value of low 'n slow and pit beef is an exercise in futility. They're completely different beasts.
If it helps, hyde, Chaps reportedly uses bottom round, though I'm led to believe that's a matter of economy and most prefer top round.
Any cut of beef from the ribs or loin will be nice and tender. If you need to save a few bucks, you might want to look at chuck, flank, etc.
Low and slow, as paul pointed out, is the only way to go - regardless of which cut of beef you select. I'm no "old" cowboy, but I don't want sugar on my meat either.
Out here in Colorado we like Beef Brisket 18 hours at 190 or Beef Chuck 16 hours @ 190
or Pork Chuck, I think they call it a Boston Butt in yankee land. 12 hours @ 190 out this
way we serve the sauce on the side for the kids. Old cowboys would be horrified if you
put sugar on their meat. Smoke with Apple wood. You only need the smoke for the
first 4 hours.