Maybe the significant difference is that the Irish song was written at the time, within days of Terence McSweeney's death in a hunger strike; the American adaptation was written a hundred years after the Civil War, but written in period, so to speak.

Good songs can indeed be written long after the events they portray, but I think the best in that category will be coloured by what has happened since.They can be a way of making more sense for a later generation of what happened long ago, and what was happening at the time they were written, maybe. ("The Night they Drove old Dixie Down", for example, couldn't have been written back in the 1860s. It's as much about the 1960s.)