There's some commentary on "While Shepherds Watched" (and its multiplicity of tunes--over 300?) in the notes and recorded intro for this clip on YouTube of "Sweet Chiming Bells". The written commentary:

This is one of the many versions of While Shepherds Watched - believed to number well in excess of 300 different tunes. Before about 1700 the only songs which were allowed to be sung in churches were those which used directly from the bible - anything else was considered to be sacrilege. Then after Nahum Tate wrote these words in 1692 the King gave a special decree that these words were worthy of being sung in church too. Every village and every church had their church band and singers and this song was often sung to other tunes used during the rest of the year like Cranbrook, which later became what we know as On Ilkley Moor Bah' tat. Sweet Chiming Christmas Bells has a chorus - one theaory is that the song comes from a funeral hymn wishing the soul on its way to heaven.