I've used antlers for over a year and haven't had problems with pieces breaking off. Maybe Lani is right that there are different levels of quality. I always supervise them though and don't leave them alone with it.
One thing about bully sticks, is your pup eating the whole thing at once? Because that could definitely be causing the diarrhea. I usually let them chew on it for 20-30 minutes and then take it away for another day because we've experienced that problem before.
Lady (1.5 year old tricolour) & Gracie (4 year old blenheim)
"Happiness is a warm puppy" - Charles M. Schulz