Hindcast simulations of MJO events during the dynamics of the MJO (DYNAMO) field campaign are conducted with two models, one with conventional parameterization (CAM5) and a comparable model that utilizes superparameterization (SP-CAM). SP-CAM is shown to produce a qualitatively better reproduction of the fluctuations of precipitation and low-level zonal wind associated with the first two DYNAMO MJO events compared to CAM5. Interestingly, skill metrics using the real-time multivariate MJO index (RMM) suggest the opposite conclusion that CAM5 has more skill than SP-CAM. This inconsistency can be explained by a systematic increase of RMM amplitude with lead time, which results from a drift of the large-scale wind field in SP-CAM that projects strongly onto the RMM index. CAM5 hindcasts exhibit a contraction of the moisture distribution, in which extreme wet and dry conditions become less frequent with lead time. SP-CAM hindcasts better reproduce the observed moisture distribution, but also have stronger drift patterns of moisture budget terms, such as an increase in drying by meridional advection in SP-CAM. This advection tendency in SP-CAM appears to be associated with enhanced off-equatorial synoptic eddy activity with lead time. Systematic drift moisture tendencies in SP-CAM are of similar magnitude to intraseasonal moisture tendencies, and therefore are important for understanding MJO prediction skill.