This is a table comparing the ENSO and QBO models. It's interesting that the QBO model is a good training for the ENSO model even though the basic formulation differs between the two.
The most significant similarity between the two is their reliance on lunisolar forcing, and in particular, a lunar forcing that is accentuated with a seasonal cycle such that the effective forcing periods are aliased versions of the known lunar monthly periods.
One of the lessons learned from this exercise is to avoid any kind of filtering on the data during the fitting process since a priori one can't distinguish noise from signal. The only filtering was done prior to accessing the data from the repository. This is unnerving because for the SOI data, the anti-correlation between the Darwin and Tahiti data appears poor (see the figure below), yet when the dipole is extracted, it must effectively remove the noise. The great unknown is how much noise remains after the model is fitted to the data.
The ultimate reason for the relative simplicity of the QBO model was that it only has one significant lunar driver in terms of the nodal or draconic tide. In contrast, the ENSO model requires all three of the lunar terms -- nodal, synodic, and anomalistic, in addition to two Earth wobble terms.