One study did find that MM gave a higher immune response in most areas than PP ( Inside Medicine. What Are You Seeing? [COVID-19 medical news] - #5260 by ucbalumnus ). This may be due to M’s higher mRNA dose than P. Note that the M-booster (or m) is half dose of M, but that is still a higher dose than P.
One study ( https://www.science.org/doi/10.1126/scitranslmed.abm2311 ) did note some differences in types of immune response between MM and PP, so there may be some vaccine diversity benefit of a different booster between the two (but probably much smaller than with a different type of vaccine like J, but now that J is officially discouraged, that vaccine diversity is no longer available).
In this case, the risk of sensitivity to ingredients in m versus P would be a possible disadvantage of m that you need to consider against the possible advantages of m listed above.