The performance of arfgen depends mainly on the number of points in the detector map that are enclosed within the said regions. This means that the coarser the detector map, the less CAL calls are made, and the less accurate the resultant ARF is. At the other extreme, a detector map that is too finely binned would result in a large number of CAL calls and would affect the execution time of the task. Ideally the binning should be such that it reflects the spatial scaling of instrumental variations across the detector, including any chip gaps and bad columns which fall within the extraction region.
The execution time is also dependent upon the actual size of the source region if chip gap and bad pixel corrections are switched on (withbadpixcorr=true). In fact this becomes the dominant contribution for large source areas.