People that are curious about CMH should look at the Univ. of Utah research. This study says the YPF (yield photon flux) of Philips HPS bulbs is 95%, the Philips CMH bulb, 90%. You multiply that number by the PAR count for each bulb to get the useable light for plants, YPF is a weighted average.
So if the PAR number for an HPS light exceeds that of a CMH bulb, the useable light for plants will be even higher with HPS. You can also see that CMH does put more of the total output into the PAR part of the spectrum than HPS, but HPS still has higher overall PAR numbers because it puts out so much more light (lumens or lux). So the HPS light puts out more net PAR, and 6% more of that light is at the spectral points utilized by plant
https://www.cycloptics.com/sites/default/files/GB USU Spectral Characterization link.pdf