I suggest that you use a quarterly periodicity because at the end of the day you're going to have to generate a quarterly forecast.
If you where to use a monthly periodicity in your model, to obtain the quarterly forecast you're going to have to make a 3-step ahead forecast. In contrast, when modeling with quarterly data, a single step ahead forecast will suffice. The single step ahead forecast is much more desirable as it will have lower variance (i.e. tighter prediction intervals). This is exacerbated if the series that you're modeling follows a unit root.
To me, this observation will greatly outweigh any potential information gains.
Further, not all additional information is good. Imagine you had hourly data instead of monthly data. There is a lot of variation between hours that is not really going to help you determine what is going to happen at the end of the quarter.