You really can't compare anywhere to Ireland. The closest you'll get is the North Island of New Zealand, where the land area is about 30% bigger, but the population is about 40% lower. But that doesn't have anywhere as heavily-populated as Europe on its doorstep, nor is it split between two states.
For what it's worth, Auckland handles about 20 million passengers, while a fairly sizable airport also exists in Wellington, which handles 6 million. They are about 600km apart though, so it's more like Cork Airport to City of Derry than Dublin to Belfast.