As a bit of fun I once ran the two songs together at our singing session at the Belvedere in Liverpool; starting with Mary Delaney's version and then Bess Cronin's, and finishing with a bit of diddling. It was very enjoyable to do, and it was lovely to watch the recognition dawn on some listeners who might have known both versions that I was singing the "same" song!
It felt a bit cheeky and I hope it wasn't disrespectful.