Jack's tune is the one that Roy Palmer set to the lyric. Bob's is the same one I linked for 'King John & the Abbott'.

I'm not sure whether the original broadside specified a tune, but the kind of melody required would be obvious from the chorus anyway. The point is that either of those 'Derry Down' tunes would fit the bill, and there were many songs set to 'Derry Down'. Harry Boardman sang 'The Dreadnought' to Jack's version.