Scott - when I refer to the 'hogged' style, I'm indicating a cavity that is generally round-bottomed from front all the way back to the inside of the buttplate, i.e. generally no web of wood between the cavity and the inside of the buttplate. Also if cut correctly, the angled walls can serve as a mating surface for the dovetail on the bottom of the box lid, so no need to cut 'rails.' A squared cavity, on the other hand, is cut just like a small box and typically retains a web of wood between the cavity and the inside of the buttplate. This type of cavity also necessitates the cutting of 'rails' to accommodate the wood lid. This would be comparable to the AA coffee mill. The short rifle and #19 are of the larger gouged/hogged variety, which Rich mentioned (I believe) because no other surviving piece attributed to Beth or CS is cut in this manner. It's a much rarer cavity type relative to surviving American guns, though fairly common in German work.
In terms of preference, there are pros and cons of both types. I can't think of any reason a customer would prefer one over another, save that the 'hogged' type is usually larger so if you're the type of shooter that carries a lot in the box, you might prefer such a cavity. As a gunsmith, I have no preference either way myself. The smaller boxed type is more time consuming to cut in my opinion because of the need for rails, but on the other hand, the gouged type (preferably) should make use of an inletted buttplate (as opposed to flat sawn at the rear) to prevent the presence of a gap or crack at the bottom of the cavity into which small pieces of 'stuff' might get lost. I guess it's 6 of one, half dozen of other in terms of time.