The two songs are unconnected, other than as to subject. The "Come Tender hearted christians.." one is definitely the earlier - O'Lochlainn refers to it in a book by Petrie in 1882 - and reckons it is near contemporary to 1798.

Regards

p.s. The Gaelic version of "Oh see the fleet foot hosts.." given in the earlier looks like a relatively recent translation.