Everything else identical, it is possible to have a slightly bigger cross-pin or a lower profile action with a through lump than with a hidden lump.
That probably explains why H&H used them on Double rifles.
A benefit of the through lump is that it is possible to see if the gun has been rejointed many times. If so, there usually is a gap in the through lump fit.
The same is true for the doll's head fitting.
Best regards,
WC-