I looked at my capper today and the metal plates (jaws) are two-sided. One end is marked 26 and the other 29. I suspect this is diameter of the bottle neck in millimeters. All the 12 ounce bottles I have that use crown caps are 26 millilmetes. A few of the larger bottles have 29 mm diameter necks.
I also found the 12 oz. bottles have some variation in the distance from the top of the bottle to the bottom of the shoulder that the metal jaws in the capper use to pull against. On most bottles this distance is less than the closed dimension of the capper, meaning the bottle is slightly loose within the capper when the capper is fully closed. This is without a cap. One bottle I had was too long and the capper fully tightens on it even without a cap. As it happens, this was a twist-off bottle.
I do not know if the bottles that I broke on me were this type or not as I was not in fault analysis mode when they broke. I cleaned up, discarding the pieces, and carried on. For now I have decided to only use bottles from certain brands of beer that I know fit in the capper well: Samuel Adams, Sierra Nevada, Kona, and Anchor all seem ok. Certainly there are many others that will work correctly.