Just guessing when I haven't seen it but, to me, it would be how much residue you have left.If it's heavy and you aren't grazing it,you may be better off to bale it.If it was thin and tall and not likely to smother the grass underneath,might be better to let it go back.
If your neighbor is needing hay and can bale some of it,you might be doing yourself a favor in the long run even if you loose some nutrients.Good deeds have a way of returning.
I have one field which gets ahead of me before I can get cattle on it some years. Grows up tall and matures.Have let the neighbors cut it on shares when they cut theirs for some extra hay.I get some hay made I don't have to handle and the field mowed off which I would have to do anyway.They get some hay they wouldn't have otherwise.Yes,I loose some of the grazable grass but I have extra hay if it gets dry I can feed back or save for winter.I look at it as a win for both of us. :2cents: