There’s a lot more that goes into vaccine design than just the main component (mRNA encoding antigen in this case). The lipid nanoparticle (LNP) that holds this mRNA is what will differentiate Moderna and Pfizer, as well as some dosage and concentration differences. Both do not have an explicit adjuvant (basically a kickstarter to get the immune response going), because the mRNA, once inside the cell, can elicit an innate immune response through a few different receptors specific for nucleic acid. Downstream, this causes transcription and expression of inflammatory cytokines and chemokines, and, therefore, a robust immune response (this is the case for both mRNA vaccines). It's also possible the lipid nanoparticle (different for each mRNA vaccine) may kind of act like an adjuvant as well. Exactly how these immune responses are initiated can make a HUGE difference in how protection is conferred. The way innate immunity reacts will affect the way the adaptive immunity reacts, and if the different LNPs of the vaccines have slightly different downstream effects, this could change the specifics of the immune response. It is also possible the differences in dosages and concentrations of mRNA between the two have created slightly different downstream effects, and, therefore, slightly different immune responses.

So, a possible reason for the difference in response/effectiveness between the two mRNA vaccines may lie within how immunity was specifically conferred, whether through differences in the LNPs, dosage, or concentrations of mRNA.

Source: doing PhD on vaccine stuff