What Michael said.
A rimmed case will always exert the same TOTAL thrust as an otherwise-identical rimless one, but the rimmed case's slightly larger head area will always result in slightly less thrust per square inch where it touches against the breech face. In a bolt rifle or falling-block SS this thrust difference is immaterial since the breeching is tighter and there is usually some camming action upon closing. However with a break-open rifle there's little camming action upon closing and so the dimensions must allow for a slightly-dirty action closing upon a slightly-oversize cartridge.
Eventually this slightly looser & more-flexible design will result in a battering of the action internals as compared to the bolt or falling block rifles. Might take a thousand rounds, might take a hundred thousand, probably won't ever become noticable at all in most instances. But the fact remains that the rimless case exacerbates this battering tendency by concentrating its thrust upon a smaller surface area than the rimmed one.
There's also the fact that a rimmed case will always be stronger than an otherwise-identical rimless one, simply because of the added hoop strength provided by the rim as opposed to the extractor groove.
Regards, Joe