The text you quote is also from Percy's Reliques, introduced as "revised and altered by a modern hand". F. J. Child (English and Scottish Popular Ballads, vol.I p.271) commented:

"The Boy and the Mantle was printed "verbatim" from his manuscript by Percy in the Reliques, III, p.3, ed. 1765. The copy at p.314 is of course the same "revised and altered" by Percy, but has sometimes been mistaken for an independent one."