I don't know an answer to your specific question, but the mesh on the right has potential rendering quality issues. The border between the two boxes is going to be "saw-toothed" to some degree because the z-buffer precision is not exact and the edge pixels of two faces are almost exactly in the same depth, as far as the hardware is concerned. Same applies to offline rendering, but generally the depth precision of software renderers is better so you may not notice the issue as often.

Remember that at this level of geometric complexity, the overhead of extra faces is very near to zero and is further masked away by other bottlenecks anyway (on any modern GPU). There are some fillrate savings as well, if the lower box actually has a hole underneath the upper box

The mesh on the right is more optimized for data transfer throughput (as in copying over network or other slow links) and limited storage, though, as there are fewer vertices.