Are there any advantages of HPS over MH or vise versa?
HPS: Cheap lamps, efficient, quite long life (limited by thermal instability, so annoying cycling EOL behavior - need to be addressed by the gear intelligence, like ignitor cut-out timers), self-compensate for lumen loss over life (on most ballasts increase it's real power input, as the lamp age), however very poor color rendering
White-SON: High quality really warm white light (the only HID available for CCT<3000K and CRI 90+), expensive lamps, quite short lifetime, complex gear (require active arctube temperature stabilization, as inherently thermally unstable), not as high efficacy
QMH-probe: White light with moderate CRI, relatively simple ballast in US (in Europe require ignitor as HPS or pulse-MH, so no advantage here), not as expensive lamps, medium lifetime, poor efficacy (worst "of this list"), life rating exaggerated due to the high lumen loss - economic life (when limited by 70% lumen output) is quite short, high risk of non-passive EOL behavior - need protection
QMH-pulse: Not as much expensive lamps (but more then HPS), quite good efficacy, in Europe compatible with HPS gear, if it is thermally protected, medium quality light (CRI 70..80), not so stable color, life not as good (limited by lumen drop), high risk of non-passive EOL behavior - need protection
CMH: Quite expensive lamp, high efficacy, quite long life (but not as HPS) good CRI (80+) for 3000K and below, excellent (90+) for ~4000K, stable color, not available in >4500K, some risk of non-passive EOL behavior - need protection