The strength of an El Nino event does seem to matter with respect to seasonal climate connections here in the Southwest. Looking at past precipitation patterns during El Nino winters of varying strengths, you notice that strong events (ones with ONI values >1.5) tend to have a more reliably wet look to them versus weak events which vary from above-average to even below-average.
The forecast of a strong El Nino event tends to lead to a subsequently more confident outlook in wet conditions for Arizona and New Mexico. If the event is forecasted to be weak or even moderate the outlook for precipitation over the upcoming winter season is much less certain (more on this topic climate.gov)
A version of this FAQ was originally published on the CLIMAS blog on Aug 13, 2014