All I have read here is repetition from the pulp gun magazines  from which I learned how to read 60+ years ago instead of Dick and Jane. Both had about the same level of content. We all know those writes knew nothing aside from regurgitating each others writings which spring from the marketing ploys of the various gun makers.  Advantages/disadvantages are dependent on too many other variables (largely the individual shooter and his preferences/training) to be defined as simply as deeper or shallower.  The Browning Superposed is about as deep as the O/Us get and it is revered. The Kreighoff M32 is about as shallow as is available and it gets hacked in some quarters for handling characteristics.  Shoot what you like once it is fitted.  The depth difference in sxs guns is insignificant unless you put on one of the big forends more appropriate to an unlimited benchrest rifle.  IMHO