Taking the USMLE (MD licensure boards) can make you more competitive for ACGME (MD) residencies. Neither the COMLEX (DO licensure boards) nor the USMLE have anything to do with board certification. They are used for state licensure and you take the 3 steps of these boards during medical school and your first year of residency.
Now, if you're talking about specialty boards that are taken after residency (family medicine, surgery, radiology, etc, etc)...you generally take the boards for the residency program you attended: meaning that if you go through an ACGME residency you're usually board certified through the MD specialty board and if you go through an AOA (DO) residency you're usually board certified through the DO specialty board. There are specialty boards for each type of residency, so the specific board depends on what area of medicine you go into.