Metal pulls use bolts, not screws.
The breakaway bolts are a convenience if your door or drawer face is much thicker or thinner than usual, savings you the hassle of getting replacement bolts to make that adjustment. On the other hand, they do have the hassle of forcing you to break them to length if they're too long as shipped, and for typical applications you don't need that adjustability.
Other than that, there really is no significant difference for this application. Pick whichever you think is least work for your application, remembering that you can always get replacement bolts (and might already have something suitable on hand).