Issue generating aligned meshes for stacked solids

I have two flat solids stacked directly on top each other (one which is an identical copy of the other). The non-matching side boundaries are curved and the meshing creates slightly different point distributions on the top an bottom edges so that the meshes on the shared interface doesn't match up. I have used BRepTools_ReShape to Replace one of the duplicated shared faces which seems to work fine, but the meshing will still not match up.

Presumably I will have to Replace the shared edges (and maybe points too) to get aligned meshing? I there some functionality that can be used to find shared edges (and points) when I have the shared face identities, or is there maybe a better approach?