Wes,

Yeah, "While Shepherds Watched" is from the Tate & Brady psalter, which meant that unlike most of the Christmas texts then popular it was kosher for the Puritans and sundry Separatists. That does help to explain its popularity (though its date, 1700-1702, makes it too recent to have had a vogue when the Puritans were actually in a position to enforce such things). In the US in my experience the Handel tune CHRISTMAS is overwhelmingly the best known for it; WINCHESTER OLD is almost as common in hymnals but much less so in sung usage.

Liland