Eh, technically it's gammon and cabbage; gammon is wet-cured ham (done in a brine), and it tastes more bacon-y than American hams. Corned beef is also brine-cured, which I suspect is why it was adopted here, to get that strong saltiness that a smoked or sugar-cured ham generally lacks.
Many modern Irish dishes include combinations of bacon and cabbage (but the bacon is back bacon, what an American would call Canadian Bacon.)