Ireland would win.
New Zealand would win.
I have to hand it to the Irish. The Irish are more experienced for combat, as the IRA is a problem in sweet beloved Ireland, and can be quiet dangerous. Resulting in the need for combat, meaning experience for the troops. Furthermore, I believe the Zealanders would be facing two forces, Ireland and the IRA. Meaning double problems in my opinion.
If not for Europe, New Zealand would probably actually win. But Ireland is more important to Europe than New Zealand. I say that as a New Zealander.....
Both countries are extremely peaceful for everyone to live in but New Zealand is very peaceful due to the fact that it's a small territory and it's a little more isolated from other countries. Therefore, New Zealand probably spends more time training its military due to the fact that there's really not that much violence in New Zealand. I've never been there but if you go there, you'll see that it's a pretty friendly and beautiful country. New Zealand is also at a more strategic and beneficial location than Ireland which probably makes it easy for them to perform military tests without interference. I don't know if what I said is accurate in any way but it's just my logic.