If you are using phenix.auto_sharpen with just a map and resolution as inputs, then it will (by default) apply an overall sharpening B-factor up to the resolution limit you supply, and then a blurring B-factor beyond that.  This means that any filtering applied to the input map will make a difference.  I haven't tested systematically, but my guess is that the better the map you start with with the better the map you'll get. So I would recommend starting with the weighted map as in Rosenthal and Henderson.  In this case phenix.auto_sharpen will basically be identifying the overall sharpening that optimizes the clarity and connectivity of the map.

If you sharpen using a model, then a different sharpening is applied at each resolution (basically as in Rosenthal and Henderson, but based on the match between model and map, not between two half-maps), so the starting map should make only a small difference.

All the best,

Tom T